Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+3x+2=0
-
Equation z^2-6*z+10=0
-
Equation x^2+5x+6=0
-
Equation -x/7+x=15/7
- Express {x} in terms of y where:
- -20*x-6*y=4
- -13*x+7*y=-15
- 5*x-14*y=-15
- -12*x-10*y=-16
- Derivative of:
- f*(x)
-
Identical expressions
- f*(x)= one / three *x^ three +a
- f multiply by (x) equally 1 divide by 3 multiply by x cubed plus a
- f multiply by (x) equally one divide by three multiply by x to the power of three plus a
- f*(x)=1/3*x3+a
- f*x=1/3*x3+a
- f*(x)=1/3*x³+a
- f*(x)=1/3*x to the power of 3+a
- f(x)=1/3x^3+a
- f(x)=1/3x3+a
- fx=1/3x3+a
- fx=1/3x^3+a
- f*(x)=1 divide by 3*x^3+a
-
Similar expressions
- f*x=(3*x^4-4*x^3-5*x+12)/x
- f*(x)=1/3*x^3-a
- x2*y(x2).diff(x2).diff(x2)=(y(x2).diff(x2))*2
- f*x=x^2/(x-4)
f*(x)=1/3*x^3+a equation
The teacher will be very surprised to see your correct solution 😉
The solution
Vieta's Theorem
rewrite the equation
$$f x = a + \frac{x^{3}}{3}$$
of
$$a x^{3} + b x^{2} + c x + d = 0$$
as reduced cubic equation
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$3 a - 3 f x + x^{3} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - 3 f$$
$$v = \frac{d}{a}$$
$$v = 3 a$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - 3 f$$
$$x_{1} x_{2} x_{3} = 3 a$$
$$f x = a + \frac{x^{3}}{3}$$
of
$$a x^{3} + b x^{2} + c x + d = 0$$
as reduced cubic equation
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$3 a - 3 f x + x^{3} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - 3 f$$
$$v = \frac{d}{a}$$
$$v = 3 a$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - 3 f$$
$$x_{1} x_{2} x_{3} = 3 a$$
The graph
Rapid solution
[src]
/ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ___________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________ \\\ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ___________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________ \\
| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\||| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\||
| / / ___________________________________________________________________________________________________________________________ \ / ___________________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|||| / / ___________________________________________________________________________________________________________________________ \ / ___________________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|||
| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------| \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------| \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|||
| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | |81*im(a) \ 2 / 81*re(a) \ 2 /||| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | |81*im(a) \ 2 / 81*re(a) \ 2 /||
| / | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------|| | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||| / | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------|| | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
| / |81*im(a) \ 2 /| |81*re(a) \ 2 /| | \ 2 2 2 2 /|| / |81*im(a) \ 2 /| |81*re(a) \ 2 /| | \ 2 2 2 2 /|
| 6 / |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 6 / |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
/ f \ | / f \ \/ \ 2 2 / \ 2 2 / \ 3 /| \/ \ 2 2 / \ 2 2 / \ 3 /
x1 = - 3*re|---------------------------------------| + I*|- 3*im|---------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| _________________________________| | | _________________________________| 3 | 3
| / _____________________ | | | / _____________________ | |
| / / 3 2 | | | / / 3 2 | |
| / \/ - 2916*f + 6561*a 81*a | | | / \/ - 2916*f + 6561*a 81*a | |
|3 / ------------------------ + ---- | | |3 / ------------------------ + ---- | |
\\/ 2 2 / \ \\/ 2 2 / /
$$x_{1} = i \left(- \frac{\sqrt[6]{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2},\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2} \right)}}{3} \right)}}{3} - 3 \operatorname{im}{\left(\frac{f}{\sqrt[3]{\frac{81 a}{2} + \frac{\sqrt{6561 a^{2} - 2916 f^{3}}}{2}}}\right)}\right) - \frac{\sqrt[6]{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2},\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2} \right)}}{3} \right)}}{3} - 3 \operatorname{re}{\left(\frac{f}{\sqrt[3]{\frac{81 a}{2} + \frac{\sqrt{6561 a^{2} - 2916 f^{3}}}{2}}}\right)}$$
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| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\|| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\||| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\|| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\||
| / / ___________________________________________________________________________________________________________________________ \ / ___________________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/||| / / ___________________________________________________________________________________________________________________________ \ / ___________________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|||| / / ___________________________________________________________________________________________________________________________ \ / ___________________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/||| / / ___________________________________________________________________________________________________________________________ \ / ___________________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|||
| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------| \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------| \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------| \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------| \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|||
| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | |81*im(a) \ 2 / 81*re(a) \ 2 /|| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | |81*im(a) \ 2 / 81*re(a) \ 2 /||| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | |81*im(a) \ 2 / 81*re(a) \ 2 /|| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | |81*im(a) \ 2 / 81*re(a) \ 2 /||
| / | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------|| | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| / | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------|| | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||| / | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------|| | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| / | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------|| | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
| / |81*im(a) \ 2 /| |81*re(a) \ 2 /| | \ 2 2 2 2 /| ___ / |81*im(a) \ 2 /| |81*re(a) \ 2 /| | \ 2 2 2 2 /|| / |81*im(a) \ 2 /| |81*re(a) \ 2 /| | \ 2 2 2 2 /| ___ / |81*im(a) \ 2 /| |81*re(a) \ 2 /| | \ 2 2 2 2 /|
| 6 / |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 6 / |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
/ f \ | / f \ \/ \ 2 2 / \ 2 2 / \ 3 / \/ \ 2 2 / \ 2 2 / \ 3 /| \/ \ 2 2 / \ 2 2 / \ 3 / \/ \ 2 2 / \ 2 2 / \ 3 /
x2 = - 3*re|-------------------------------------------------------| + I*|- 3*im|-------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| _________________________________| | | _________________________________| 6 6 | 6 6
| / _____________________ | | | / _____________________ | |
|/ ___\ / / 3 2 | | |/ ___\ / / 3 2 | |
|| 1 I*\/ 3 | / \/ - 2916*f + 6561*a 81*a | | || 1 I*\/ 3 | / \/ - 2916*f + 6561*a 81*a | |
||- - - -------|*3 / ------------------------ + ---- | | ||- - - -------|*3 / ------------------------ + ---- | |
\\ 2 2 / \/ 2 2 / \ \\ 2 2 / \/ 2 2 / /
$$x_{2} = - \frac{\sqrt{3} \sqrt[6]{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2},\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2} \right)}}{3} \right)}}{6} + \frac{\sqrt[6]{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2},\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2} \right)}}{3} \right)}}{6} + i \left(\frac{\sqrt[6]{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2},\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2} \right)}}{3} \right)}}{6} + \frac{\sqrt{3} \sqrt[6]{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2},\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2} \right)}}{3} \right)}}{6} - 3 \operatorname{im}{\left(\frac{f}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{81 a}{2} + \frac{\sqrt{6561 a^{2} - 2916 f^{3}}}{2}}}\right)}\right) - 3 \operatorname{re}{\left(\frac{f}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{81 a}{2} + \frac{\sqrt{6561 a^{2} - 2916 f^{3}}}{2}}}\right)}$$
/ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ___________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________ \\ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ___________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________ \\\ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ___________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________ \\ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ___________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________ \\
| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\|| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\||| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\|| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\||
| / / ___________________________________________________________________________________________________________________________ \ / ___________________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/||| / / ___________________________________________________________________________________________________________________________ \ / ___________________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|||| / / ___________________________________________________________________________________________________________________________ \ / ___________________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/||| / / ___________________________________________________________________________________________________________________________ \ / ___________________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|||
| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------| \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------| \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------| \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------| \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|||
| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | |81*im(a) \ 2 / 81*re(a) \ 2 /|| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | |81*im(a) \ 2 / 81*re(a) \ 2 /||| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | |81*im(a) \ 2 / 81*re(a) \ 2 /|| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a), - 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/|| | |81*im(a) \ 2 / 81*re(a) \ 2 /||
| / | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------|| | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| / | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------|| | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||| / | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------|| | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| / | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *sin|-------------------------------------------------------------------------------------------------------------------------|| | \/ \2916*im (f) - 8748*re (f)*im(f) + 13122*im(a)*re(a)/ + \- 6561*im (a) - 2916*re (f) + 6561*re (a) + 8748*im (f)*re(f)/ *cos|-------------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
| / |81*im(a) \ 2 /| |81*re(a) \ 2 /| | \ 2 2 2 2 /| ___ / |81*im(a) \ 2 /| |81*re(a) \ 2 /| | \ 2 2 2 2 /|| / |81*im(a) \ 2 /| |81*re(a) \ 2 /| | \ 2 2 2 2 /| ___ / |81*im(a) \ 2 /| |81*re(a) \ 2 /| | \ 2 2 2 2 /|
| 6 / |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 6 / |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
/ f \ | / f \ \/ \ 2 2 / \ 2 2 / \ 3 / \/ \ 2 2 / \ 2 2 / \ 3 /| \/ \ 2 2 / \ 2 2 / \ 3 / \/ \ 2 2 / \ 2 2 / \ 3 /
x3 = - 3*re|-------------------------------------------------------| + I*|- 3*im|-------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| _________________________________| | | _________________________________| 6 6 | 6 6
| / _____________________ | | | / _____________________ | |
|/ ___\ / / 3 2 | | |/ ___\ / / 3 2 | |
|| 1 I*\/ 3 | / \/ - 2916*f + 6561*a 81*a | | || 1 I*\/ 3 | / \/ - 2916*f + 6561*a 81*a | |
||- - + -------|*3 / ------------------------ + ---- | | ||- - + -------|*3 / ------------------------ + ---- | |
\\ 2 2 / \/ 2 2 / \ \\ 2 2 / \/ 2 2 / /
$$x_{3} = \frac{\sqrt{3} \sqrt[6]{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2},\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2} \right)}}{3} \right)}}{6} + \frac{\sqrt[6]{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2},\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2} \right)}}{3} \right)}}{6} + i \left(\frac{\sqrt[6]{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2},\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2} \right)}}{3} \right)}}{6} - \frac{\sqrt{3} \sqrt[6]{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{im}{\left(a\right)}}{2},\frac{\sqrt[4]{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3}\right)^{2} + \left(6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(13122 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 8748 \left(\operatorname{re}{\left(f\right)}\right)^{2} \operatorname{im}{\left(f\right)} + 2916 \left(\operatorname{im}{\left(f\right)}\right)^{3},6561 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2916 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 8748 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 6561 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{81 \operatorname{re}{\left(a\right)}}{2} \right)}}{3} \right)}}{6} - 3 \operatorname{im}{\left(\frac{f}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{81 a}{2} + \frac{\sqrt{6561 a^{2} - 2916 f^{3}}}{2}}}\right)}\right) - 3 \operatorname{re}{\left(\frac{f}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{81 a}{2} + \frac{\sqrt{6561 a^{2} - 2916 f^{3}}}{2}}}\right)}$$
x3 = sqrt(3)*((((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*sin(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*im(a)/2)^2 + (((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*cos(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*re(a)/2)^2)^(1/6)*sin(atan2(((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*sin(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*im(a)/2, ((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*cos(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*re(a)/2)/3)/6 + ((((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*sin(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*im(a)/2)^2 + (((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*cos(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*re(a)/2)^2)^(1/6)*cos(atan2(((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*sin(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*im(a)/2, ((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*cos(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*re(a)/2)/3)/6 + i*(((((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*sin(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*im(a)/2)^2 + (((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*cos(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*re(a)/2)^2)^(1/6)*sin(atan2(((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*sin(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*im(a)/2, ((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*cos(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*re(a)/2)/3)/6 - sqrt(3)*((((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*sin(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*im(a)/2)^2 + (((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*cos(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*re(a)/2)^2)^(1/6)*cos(atan2(((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*sin(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*im(a)/2, ((13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3)^2 + (6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)^2)^(1/4)*cos(atan2(13122*re(a)*im(a) - 8748*re(f)^2*im(f) + 2916*im(f)^3, 6561*re(a)^2 - 2916*re(f)^3 + 8748*re(f)*im(f)^2 - 6561*im(a)^2)/2)/2 + 81*re(a)/2)/3)/6 - 3*im(f/((-1/2 + sqrt(3)*i/2)*(81*a/2 + sqrt(6561*a^2 - 2916*f^3)/2)^(1/3)))) - 3*re(f/((-1/2 + sqrt(3)*i/2)*(81*a/2 + sqrt(6561*a^2 - 2916*f^3)/2)^(1/3))))