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How to use it?
- Equation:
-
Equation z^5=-1
- Equation 4y^2-12y=0
- Equation 9x^3-18x=x-2
-
Equation x^4+x^2=0
- Express {x} in terms of y where:
- 9*x+18*y=6
- 15*x-15*y=16
- sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
- (x^2+y^2-1)^3+x^2*y^3=0
- Derivative of:
- x-2
- The double integral of:
- x-2
- Graphing y =:
- x-2
-
Identical expressions
- 9x^ three -18x=x- two
- 9x cubed minus 18x equally x minus 2
- 9x to the power of three minus 18x equally x minus two
- 9x3-18x=x-2
- 9x³-18x=x-2
- 9x to the power of 3-18x=x-2
-
Similar expressions
- 9x^3-18x=x+2
- 9x^3+18x=x-2
9x^3-18x=x-2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Vieta's Theorem
rewrite the equation
$$9 x^{3} - 18 x = x - 2$$
of
$$a x^{3} + b x^{2} + c x + d = 0$$
as reduced cubic equation
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - \frac{19 x}{9} + \frac{2}{9} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{19}{9}$$
$$v = \frac{d}{a}$$
$$v = \frac{2}{9}$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{19}{9}$$
$$x_{1} x_{2} x_{3} = \frac{2}{9}$$
$$9 x^{3} - 18 x = x - 2$$
of
$$a x^{3} + b x^{2} + c x + d = 0$$
as reduced cubic equation
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - \frac{19 x}{9} + \frac{2}{9} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{19}{9}$$
$$v = \frac{d}{a}$$
$$v = \frac{2}{9}$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{19}{9}$$
$$x_{1} x_{2} x_{3} = \frac{2}{9}$$
Sum and product of roots
[src]
sum
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
19*re|---------------------------------------| | 19*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\ 19*re|---------------------------------------| | 19*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| __________________ | | | __________________ | | |2*\/ 4962 || | |2*\/ 4962 ||| | |2*\/ 4962 || | |2*\/ 4962 || | __________________ | | | __________________ | | |2*\/ 4962 || | |2*\/ 4962 ||| | |2*\/ 4962 || | |2*\/ 4962 || __________________
| / ______ / ___\| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| | / ______ / ___\| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| / ______
| / 2*I*\/ 4962 | 1 I*\/ 3 || | | / 2*I*\/ 4962 | 1 I*\/ 3 || ____ | \ 27 /| ____ | \ 27 /|| ____ | \ 27 /| ____ | \ 27 /| | / 2*I*\/ 4962 | 1 I*\/ 3 || | | / 2*I*\/ 4962 | 1 I*\/ 3 || ____ | \ 27 /| ____ | \ 27 /|| ____ | \ 27 /| ____ | \ 27 /| / 2*I*\/ 4962
|3 / 3 + ------------ *|- - - -------|| | |3 / 3 + ------------ *|- - - -------|| \/ 19 *cos|----------------| \/ 57 *sin|----------------|| \/ 19 *sin|----------------| \/ 57 *cos|----------------| |3 / 3 + ------------ *|- - + -------|| | |3 / 3 + ------------ *|- - + -------|| \/ 19 *cos|----------------| \/ 57 *sin|----------------|| \/ 19 *sin|----------------| \/ 57 *cos|----------------| 3 / 3 + ------------
\\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 / \\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 / 19 \/ 9
- ---------------------------------------------- + I*|- ---------------------------------------------- + ---------------------------- + ----------------------------| - ---------------------------- + ---------------------------- + - ---------------------------------------------- + I*|- ---------------------------------------------- - ---------------------------- + ----------------------------| + ---------------------------- + ---------------------------- + - ------------------------- - -----------------------
9 \ 9 6 18 / 6 18 9 \ 9 6 18 / 6 18 __________________ 3
/ ______
/ 2*I*\/ 4962
9*3 / 3 + ------------
\/ 9
$$\left(\left(- \frac{\sqrt{19} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + i \left(- \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6}\right)\right) + \left(\frac{\sqrt{19} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + i \left(- \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9}\right)\right)\right) + \left(- \frac{\sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}{3} - \frac{19}{9 \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
19*re|---------------------------------------| 19*re|---------------------------------------| | 19*im|---------------------------------------| / / ______\\ / / ______\\| | 19*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\
| __________________ | | __________________ | __________________ | | __________________ | | |2*\/ 4962 || | |2*\/ 4962 ||| | | __________________ | | |2*\/ 4962 || | |2*\/ 4962 ||| | |2*\/ 4962 ||
| / ______ / ___\| | / ______ / ___\| / ______ | | / ______ / ___\| |atan|----------|| |atan|----------||| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------||
| / 2*I*\/ 4962 | 1 I*\/ 3 || | / 2*I*\/ 4962 | 1 I*\/ 3 || / 2*I*\/ 4962 | | / 2*I*\/ 4962 | 1 I*\/ 3 || ____ | \ 27 /| ____ | \ 27 /|| | | / 2*I*\/ 4962 | 1 I*\/ 3 || ____ | \ 27 /| ____ | \ 27 /|| ____ | \ 27 /|
|3 / 3 + ------------ *|- - + -------|| |3 / 3 + ------------ *|- - - -------|| 3 / 3 + ------------ | |3 / 3 + ------------ *|- - + -------|| \/ 19 *cos|----------------| \/ 57 *sin|----------------|| | |3 / 3 + ------------ *|- - - -------|| \/ 19 *cos|----------------| \/ 57 *sin|----------------|| \/ 57 *cos|----------------|
19 \\/ 9 \ 2 2 // \\/ 9 \ 2 2 // \/ 9 | \\/ 9 \ 2 2 // \ 3 / \ 3 /| | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 /
- ------------------------- - ---------------------------------------------- - ---------------------------------------------- - ----------------------- + I*|- ---------------------------------------------- - ---------------------------- + ----------------------------| + I*|- ---------------------------------------------- + ---------------------------- + ----------------------------| + ----------------------------
__________________ 9 9 3 \ 9 6 18 / \ 9 6 18 / 9
/ ______
/ 2*I*\/ 4962
9*3 / 3 + ------------
\/ 9
$$- \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{9} - \frac{\sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}{3} + i \left(- \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9}\right) + i \left(- \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6}\right) - \frac{19}{9 \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}$$
product
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 19*re|---------------------------------------| | 19*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\| | 19*re|---------------------------------------| | 19*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\|
| | __________________ | | | __________________ | | |2*\/ 4962 || | |2*\/ 4962 ||| | |2*\/ 4962 || | |2*\/ 4962 ||| | | __________________ | | | __________________ | | |2*\/ 4962 || | |2*\/ 4962 ||| | |2*\/ 4962 || | |2*\/ 4962 ||| / __________________\
| | / ______ / ___\| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | | / ______ / ___\| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | / ______ |
| | / 2*I*\/ 4962 | 1 I*\/ 3 || | | / 2*I*\/ 4962 | 1 I*\/ 3 || ____ | \ 27 /| ____ | \ 27 /|| ____ | \ 27 /| ____ | \ 27 /|| | | / 2*I*\/ 4962 | 1 I*\/ 3 || | | / 2*I*\/ 4962 | 1 I*\/ 3 || ____ | \ 27 /| ____ | \ 27 /|| ____ | \ 27 /| ____ | \ 27 /|| | / 2*I*\/ 4962 |
| |3 / 3 + ------------ *|- - - -------|| | |3 / 3 + ------------ *|- - - -------|| \/ 19 *cos|----------------| \/ 57 *sin|----------------|| \/ 19 *sin|----------------| \/ 57 *cos|----------------|| | |3 / 3 + ------------ *|- - + -------|| | |3 / 3 + ------------ *|- - + -------|| \/ 19 *cos|----------------| \/ 57 *sin|----------------|| \/ 19 *sin|----------------| \/ 57 *cos|----------------|| | 3 / 3 + ------------ |
| \\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /| | \\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /| | 19 \/ 9 |
|- ---------------------------------------------- + I*|- ---------------------------------------------- + ---------------------------- + ----------------------------| - ---------------------------- + ----------------------------|*|- ---------------------------------------------- + I*|- ---------------------------------------------- - ---------------------------- + ----------------------------| + ---------------------------- + ----------------------------|*|- ------------------------- - -----------------------|
\ 9 \ 9 6 18 / 6 18 / \ 9 \ 9 6 18 / 6 18 / | __________________ 3 |
| / ______ |
| / 2*I*\/ 4962 |
| 9*3 / 3 + ------------ |
\ \/ 9 /
$$\left(- \frac{\sqrt{19} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + i \left(- \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6}\right)\right) \left(\frac{\sqrt{19} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + i \left(- \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9}\right)\right) \left(- \frac{\sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}{3} - \frac{19}{9 \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)$$
=
/ / / ______\\\
| | |2*\/ 4962 |||
| |2*atan|----------||| / 2/3 \
3 ___ | | \ 27 /|| |/ ______\ 3 ___|
19*\/ 3 *|1 - 2*cos|------------------||*\\27 + 2*I*\/ 4962 / + 19*\/ 3 /
\ \ 3 //
----------------------------------------------------------------------------
___________________
3 / ______
243*\/ 27 + 2*I*\/ 4962
$$\frac{19 \sqrt[3]{3} \left(1 - 2 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}\right) \left(19 \sqrt[3]{3} + \left(27 + 2 \sqrt{4962} i\right)^{\frac{2}{3}}\right)}{243 \sqrt[3]{27 + 2 \sqrt{4962} i}}$$
19*3^(1/3)*(1 - 2*cos(2*atan(2*sqrt(4962)/27)/3))*((27 + 2*i*sqrt(4962))^(2/3) + 19*3^(1/3))/(243*(27 + 2*i*sqrt(4962))^(1/3))
Rapid solution
[src]
/ 1 \ / / 1 \ \
19*re|---------------------------------------| | 19*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| __________________ | | | __________________ | | |2*\/ 4962 || | |2*\/ 4962 ||| | |2*\/ 4962 || | |2*\/ 4962 ||
| / ______ / ___\| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
| / 2*I*\/ 4962 | 1 I*\/ 3 || | | / 2*I*\/ 4962 | 1 I*\/ 3 || ____ | \ 27 /| ____ | \ 27 /|| ____ | \ 27 /| ____ | \ 27 /|
|3 / 3 + ------------ *|- - - -------|| | |3 / 3 + ------------ *|- - - -------|| \/ 19 *cos|----------------| \/ 57 *sin|----------------|| \/ 19 *sin|----------------| \/ 57 *cos|----------------|
\\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = - ---------------------------------------------- + I*|- ---------------------------------------------- + ---------------------------- + ----------------------------| - ---------------------------- + ----------------------------
9 \ 9 6 18 / 6 18
$$x_{1} = - \frac{\sqrt{19} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + i \left(- \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6}\right)$$
/ 1 \ / / 1 \ \
19*re|---------------------------------------| | 19*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| __________________ | | | __________________ | | |2*\/ 4962 || | |2*\/ 4962 ||| | |2*\/ 4962 || | |2*\/ 4962 ||
| / ______ / ___\| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
| / 2*I*\/ 4962 | 1 I*\/ 3 || | | / 2*I*\/ 4962 | 1 I*\/ 3 || ____ | \ 27 /| ____ | \ 27 /|| ____ | \ 27 /| ____ | \ 27 /|
|3 / 3 + ------------ *|- - + -------|| | |3 / 3 + ------------ *|- - + -------|| \/ 19 *cos|----------------| \/ 57 *sin|----------------|| \/ 19 *sin|----------------| \/ 57 *cos|----------------|
\\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = - ---------------------------------------------- + I*|- ---------------------------------------------- - ---------------------------- + ----------------------------| + ---------------------------- + ----------------------------
9 \ 9 6 18 / 6 18
$$x_{2} = \frac{\sqrt{19} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + i \left(- \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9}\right)$$
__________________
/ ______
/ 2*I*\/ 4962
3 / 3 + ------------
19 \/ 9
x3 = - ------------------------- - -----------------------
__________________ 3
/ ______
/ 2*I*\/ 4962
9*3 / 3 + ------------
\/ 9
$$x_{3} = - \frac{\sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}{3} - \frac{19}{9 \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}$$
x3 = -(3 + 2*sqrt(4962)*i/9)^(1/3)/3 - 19/(9*(3 + 2*sqrt(4962)*i/9)^(1/3))
Numerical answer
[src]
x1 = -1.50298536069965
x2 = 0.10582452622341
x3 = 1.39716083447624
x3 = 1.39716083447624