Mister Exam
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How to use it?
- Equation:
-
Equation cos(x)=-3
-
Equation x²-6x+5=0
-
Equation (5+7*a)*15=-30
-
Equation 1/2x=5
- Express {x} in terms of y where:
- -19*x-10*y=-10
- -3*x-18*y=-15
- 20*x-10*y=6
- 17*x-8*y=8
-
Identical expressions
- x^ three /(one / one thousand)-x- two / ten ^ twenty-two = zero
- x cubed divide by (1 divide by 1000) minus x minus 2 divide by 10 squared 2 equally 0
- x to the power of three divide by (one divide by one thousand) minus x minus two divide by ten to the power of twenty minus two equally zero
- x3/(1/1000)-x-2/1022=0
- x3/1/1000-x-2/1022=0
- x³/(1/1000)-x-2/10²2=0
- x to the power of 3/(1/1000)-x-2/10 to the power of 22=0
- x^3/1/1000-x-2/10^22=0
- x^3/(1/1000)-x-2/10^22=O
- x^3 divide by (1 divide by 1000)-x-2 divide by 10^22=0
-
Similar expressions
- x^3/(1/1000)+x-2/10^22=0
- x^3/(1/1000)-x+2/10^22=0
x^3/(1/1000)-x-2/10^22=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
3
x 1
------ - x - --- = 0
1/1000 22
5
3
x 1
------ - x - --- = 0
1/1000 22
5
Vieta's Theorem
rewrite the equation
of
$$a x^{3} + b x^{2} + c x + d = 0$$
as reduced cubic equation
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - \frac{x}{1000} - \frac{1}{2384185791015625000} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{1000}$$
$$v = \frac{d}{a}$$
$$v = - \frac{1}{2384185791015625000}$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{1}{1000}$$
$$x_{1} x_{2} x_{3} = - \frac{1}{2384185791015625000}$$
3
x 1
------ - x - --- = 0
1/1000 22
5 of
$$a x^{3} + b x^{2} + c x + d = 0$$
as reduced cubic equation
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - \frac{x}{1000} - \frac{1}{2384185791015625000} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{1000}$$
$$v = \frac{d}{a}$$
$$v = - \frac{1}{2384185791015625000}$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{1}{1000}$$
$$x_{1} x_{2} x_{3} = - \frac{1}{2384185791015625000}$$
Rapid solution
[src]
/ 1 \ / / 1 \ \
re|---------------------------------------------------------------------------------| |im|---------------------------------------------------------------------------------| / / ________________________________\\ / / ________________________________\\| / / ________________________________\\ / / ________________________________\\
| ____________________________________________________________| | | ____________________________________________________________| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 ||| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 ||
|/ ___\ / ________________________________ | | |/ ___\ / ________________________________ | |atan|----------------------------------|| |atan|----------------------------------||| |atan|----------------------------------|| |atan|----------------------------------||
|| 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | | || 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | ____ | \ 18 /| ____ | \ 18 /|| ____ | \ 18 /| ____ | \ 18 /|
||- - - -------|*3 / ------------------- + ------------------------------------ | | ||- - - -------|*3 / ------------------- + ------------------------------------ | \/ 10 *cos|----------------------------------------| \/ 30 *sin|----------------------------------------|| \/ 30 *cos|----------------------------------------| \/ 10 *sin|----------------------------------------|
\\ 2 2 / \/ 4768371582031250000 85830688476562500000 / | \\ 2 2 / \/ 4768371582031250000 85830688476562500000 / \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = ------------------------------------------------------------------------------------- + I*|------------------------------------------------------------------------------------- - ---------------------------------------------------- - ----------------------------------------------------| - ---------------------------------------------------- + ----------------------------------------------------
3000 \ 3000 200 600 / 600 200
$$x_{1} = - \frac{\sqrt{30} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000} + \frac{\sqrt{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200} + i \left(- \frac{\sqrt{10} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200} - \frac{\sqrt{30} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} + \frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000}\right)$$
/ 1 \ / / 1 \ \
re|---------------------------------------------------------------------------------| |im|---------------------------------------------------------------------------------| / / ________________________________\\ / / ________________________________\\| / / ________________________________\\ / / ________________________________\\
| ____________________________________________________________| | | ____________________________________________________________| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 ||| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 ||
|/ ___\ / ________________________________ | | |/ ___\ / ________________________________ | |atan|----------------------------------|| |atan|----------------------------------||| |atan|----------------------------------|| |atan|----------------------------------||
|| 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | | || 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | ____ | \ 18 /| ____ | \ 18 /|| ____ | \ 18 /| ____ | \ 18 /|
||- - + -------|*3 / ------------------- + ------------------------------------ | | ||- - + -------|*3 / ------------------- + ------------------------------------ | \/ 30 *sin|----------------------------------------| \/ 10 *cos|----------------------------------------|| \/ 10 *sin|----------------------------------------| \/ 30 *cos|----------------------------------------|
\\ 2 2 / \/ 4768371582031250000 85830688476562500000 / | \\ 2 2 / \/ 4768371582031250000 85830688476562500000 / \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = ------------------------------------------------------------------------------------- + I*|------------------------------------------------------------------------------------- - ---------------------------------------------------- + ----------------------------------------------------| - ---------------------------------------------------- - ----------------------------------------------------
3000 \ 3000 600 200 / 200 600
$$x_{2} = \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000} - \frac{\sqrt{30} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} - \frac{\sqrt{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200} + i \left(\frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000} - \frac{\sqrt{30} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} + \frac{\sqrt{10} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200}\right)$$
____________________________________________________________
/ ________________________________
/ 1 I*\/ 272848410531878471374511718426 1
x3 = 3 / ------------------- + ------------------------------------ + ----------------------------------------------------------------------
\/ 4768371582031250000 85830688476562500000 ____________________________________________________________
/ ________________________________
/ 1 I*\/ 272848410531878471374511718426
3000*3 / ------------------- + ------------------------------------
\/ 4768371582031250000 85830688476562500000
$$x_{3} = \frac{1}{3000 \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}} + \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}$$
x3 = 1/(3000*(1/4768371582031250000 + sqrt(272848410531878471374511718426)*i/85830688476562500000)^(1/3)) + (1/4768371582031250000 + sqrt(272848410531878471374511718426)*i/85830688476562500000)^(1/3)
Sum and product of roots
[src]
sum
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
re|---------------------------------------------------------------------------------| |im|---------------------------------------------------------------------------------| / / ________________________________\\ / / ________________________________\\| / / ________________________________\\ / / ________________________________\\ re|---------------------------------------------------------------------------------| |im|---------------------------------------------------------------------------------| / / ________________________________\\ / / ________________________________\\| / / ________________________________\\ / / ________________________________\\
| ____________________________________________________________| | | ____________________________________________________________| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 ||| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 || | ____________________________________________________________| | | ____________________________________________________________| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 ||| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 ||
|/ ___\ / ________________________________ | | |/ ___\ / ________________________________ | |atan|----------------------------------|| |atan|----------------------------------||| |atan|----------------------------------|| |atan|----------------------------------|| |/ ___\ / ________________________________ | | |/ ___\ / ________________________________ | |atan|----------------------------------|| |atan|----------------------------------||| |atan|----------------------------------|| |atan|----------------------------------||
|| 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | | || 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | ____ | \ 18 /| ____ | \ 18 /|| ____ | \ 18 /| ____ | \ 18 /| || 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | | || 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | ____ | \ 18 /| ____ | \ 18 /|| ____ | \ 18 /| ____ | \ 18 /| ____________________________________________________________
||- - - -------|*3 / ------------------- + ------------------------------------ | | ||- - - -------|*3 / ------------------- + ------------------------------------ | \/ 10 *cos|----------------------------------------| \/ 30 *sin|----------------------------------------|| \/ 30 *cos|----------------------------------------| \/ 10 *sin|----------------------------------------| ||- - + -------|*3 / ------------------- + ------------------------------------ | | ||- - + -------|*3 / ------------------- + ------------------------------------ | \/ 30 *sin|----------------------------------------| \/ 10 *cos|----------------------------------------|| \/ 10 *sin|----------------------------------------| \/ 30 *cos|----------------------------------------| / ________________________________
\\ 2 2 / \/ 4768371582031250000 85830688476562500000 / | \\ 2 2 / \/ 4768371582031250000 85830688476562500000 / \ 3 / \ 3 /| \ 3 / \ 3 / \\ 2 2 / \/ 4768371582031250000 85830688476562500000 / | \\ 2 2 / \/ 4768371582031250000 85830688476562500000 / \ 3 / \ 3 /| \ 3 / \ 3 / / 1 I*\/ 272848410531878471374511718426 1
------------------------------------------------------------------------------------- + I*|------------------------------------------------------------------------------------- - ---------------------------------------------------- - ----------------------------------------------------| - ---------------------------------------------------- + ---------------------------------------------------- + ------------------------------------------------------------------------------------- + I*|------------------------------------------------------------------------------------- - ---------------------------------------------------- + ----------------------------------------------------| - ---------------------------------------------------- - ---------------------------------------------------- + 3 / ------------------- + ------------------------------------ + ----------------------------------------------------------------------
3000 \ 3000 200 600 / 600 200 3000 \ 3000 600 200 / 200 600 \/ 4768371582031250000 85830688476562500000 ____________________________________________________________
/ ________________________________
/ 1 I*\/ 272848410531878471374511718426
3000*3 / ------------------- + ------------------------------------
\/ 4768371582031250000 85830688476562500000
$$\left(\frac{1}{3000 \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}} + \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}\right) + \left(\left(- \frac{\sqrt{30} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000} + \frac{\sqrt{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200} + i \left(- \frac{\sqrt{10} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200} - \frac{\sqrt{30} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} + \frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000}\right)\right) + \left(\frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000} - \frac{\sqrt{30} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} - \frac{\sqrt{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200} + i \left(\frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000} - \frac{\sqrt{30} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} + \frac{\sqrt{10} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200}\right)\right)\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
re|---------------------------------------------------------------------------------| re|---------------------------------------------------------------------------------| |im|---------------------------------------------------------------------------------| / / ________________________________\\ / / ________________________________\\| |im|---------------------------------------------------------------------------------| / / ________________________________\\ / / ________________________________\\| / / ________________________________\\
| ____________________________________________________________| | ____________________________________________________________| | | ____________________________________________________________| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 ||| | | ____________________________________________________________| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 ||| | |\/ 272848410531878471374511718426 ||
|/ ___\ / ________________________________ | |/ ___\ / ________________________________ | | |/ ___\ / ________________________________ | |atan|----------------------------------|| |atan|----------------------------------||| | |/ ___\ / ________________________________ | |atan|----------------------------------|| |atan|----------------------------------||| |atan|----------------------------------||
____________________________________________________________ || 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | || 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | | || 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | ____ | \ 18 /| ____ | \ 18 /|| | || 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | ____ | \ 18 /| ____ | \ 18 /|| ____ | \ 18 /|
/ ________________________________ ||- - + -------|*3 / ------------------- + ------------------------------------ | ||- - - -------|*3 / ------------------- + ------------------------------------ | | ||- - + -------|*3 / ------------------- + ------------------------------------ | \/ 30 *sin|----------------------------------------| \/ 10 *cos|----------------------------------------|| | ||- - - -------|*3 / ------------------- + ------------------------------------ | \/ 10 *cos|----------------------------------------| \/ 30 *sin|----------------------------------------|| \/ 30 *cos|----------------------------------------|
/ 1 I*\/ 272848410531878471374511718426 1 \\ 2 2 / \/ 4768371582031250000 85830688476562500000 / \\ 2 2 / \/ 4768371582031250000 85830688476562500000 / | \\ 2 2 / \/ 4768371582031250000 85830688476562500000 / \ 3 / \ 3 /| | \\ 2 2 / \/ 4768371582031250000 85830688476562500000 / \ 3 / \ 3 /| \ 3 /
3 / ------------------- + ------------------------------------ + ---------------------------------------------------------------------- + ------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------- + I*|------------------------------------------------------------------------------------- - ---------------------------------------------------- + ----------------------------------------------------| + I*|------------------------------------------------------------------------------------- - ---------------------------------------------------- - ----------------------------------------------------| - ----------------------------------------------------
\/ 4768371582031250000 85830688476562500000 ____________________________________________________________ 3000 3000 \ 3000 600 200 / \ 3000 200 600 / 300
/ ________________________________
/ 1 I*\/ 272848410531878471374511718426
3000*3 / ------------------- + ------------------------------------
\/ 4768371582031250000 85830688476562500000
$$- \frac{\sqrt{30} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{300} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000} + \frac{1}{3000 \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}} + i \left(- \frac{\sqrt{10} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200} - \frac{\sqrt{30} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} + \frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000}\right) + i \left(\frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000} - \frac{\sqrt{30} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} + \frac{\sqrt{10} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200}\right) + \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}$$
product
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
|re|---------------------------------------------------------------------------------| |im|---------------------------------------------------------------------------------| / / ________________________________\\ / / ________________________________\\| / / ________________________________\\ / / ________________________________\\| |re|---------------------------------------------------------------------------------| |im|---------------------------------------------------------------------------------| / / ________________________________\\ / / ________________________________\\| / / ________________________________\\ / / ________________________________\\|
| | ____________________________________________________________| | | ____________________________________________________________| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 ||| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 ||| | | ____________________________________________________________| | | ____________________________________________________________| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 ||| | |\/ 272848410531878471374511718426 || | |\/ 272848410531878471374511718426 |||
| |/ ___\ / ________________________________ | | |/ ___\ / ________________________________ | |atan|----------------------------------|| |atan|----------------------------------||| |atan|----------------------------------|| |atan|----------------------------------||| | |/ ___\ / ________________________________ | | |/ ___\ / ________________________________ | |atan|----------------------------------|| |atan|----------------------------------||| |atan|----------------------------------|| |atan|----------------------------------|||
| || 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | | || 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | ____ | \ 18 /| ____ | \ 18 /|| ____ | \ 18 /| ____ | \ 18 /|| | || 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | | || 1 I*\/ 3 | / 1 I*\/ 272848410531878471374511718426 | ____ | \ 18 /| ____ | \ 18 /|| ____ | \ 18 /| ____ | \ 18 /|| / ____________________________________________________________ \
| ||- - - -------|*3 / ------------------- + ------------------------------------ | | ||- - - -------|*3 / ------------------- + ------------------------------------ | \/ 10 *cos|----------------------------------------| \/ 30 *sin|----------------------------------------|| \/ 30 *cos|----------------------------------------| \/ 10 *sin|----------------------------------------|| | ||- - + -------|*3 / ------------------- + ------------------------------------ | | ||- - + -------|*3 / ------------------- + ------------------------------------ | \/ 30 *sin|----------------------------------------| \/ 10 *cos|----------------------------------------|| \/ 10 *sin|----------------------------------------| \/ 30 *cos|----------------------------------------|| | / ________________________________ |
| \\ 2 2 / \/ 4768371582031250000 85830688476562500000 / | \\ 2 2 / \/ 4768371582031250000 85830688476562500000 / \ 3 / \ 3 /| \ 3 / \ 3 /| | \\ 2 2 / \/ 4768371582031250000 85830688476562500000 / | \\ 2 2 / \/ 4768371582031250000 85830688476562500000 / \ 3 / \ 3 /| \ 3 / \ 3 /| | / 1 I*\/ 272848410531878471374511718426 1 |
|------------------------------------------------------------------------------------- + I*|------------------------------------------------------------------------------------- - ---------------------------------------------------- - ----------------------------------------------------| - ---------------------------------------------------- + ----------------------------------------------------|*|------------------------------------------------------------------------------------- + I*|------------------------------------------------------------------------------------- - ---------------------------------------------------- + ----------------------------------------------------| - ---------------------------------------------------- - ----------------------------------------------------|*|3 / ------------------- + ------------------------------------ + ----------------------------------------------------------------------|
\ 3000 \ 3000 200 600 / 600 200 / \ 3000 \ 3000 600 200 / 200 600 / |\/ 4768371582031250000 85830688476562500000 ____________________________________________________________|
| / ________________________________ |
| / 1 I*\/ 272848410531878471374511718426 |
| 3000*3 / ------------------- + ------------------------------------ |
\ \/ 4768371582031250000 85830688476562500000 /
$$\left(- \frac{\sqrt{30} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000} + \frac{\sqrt{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200} + i \left(- \frac{\sqrt{10} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200} - \frac{\sqrt{30} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} + \frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000}\right)\right) \left(\frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000} - \frac{\sqrt{30} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} - \frac{\sqrt{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200} + i \left(\frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}}\right)}}{3000} - \frac{\sqrt{30} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{600} + \frac{\sqrt{10} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}}{200}\right)\right) \left(\frac{1}{3000 \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}} + \sqrt[3]{\frac{1}{4768371582031250000} + \frac{\sqrt{272848410531878471374511718426} i}{85830688476562500000}}\right)$$
=
/ / / ________________________________\\\
| | |\/ 272848410531878471374511718426 |||
| |2*atan|----------------------------------||| / 2/3\
| | \ 18 /|| | 3 _____ 3 _____ / ________________________________\ |
|-1 + 2*cos|------------------------------------------||*\6103515625*\/ 180 + \/ 150 *\18 + I*\/ 272848410531878471374511718426 / /
\ \ 3 //
--------------------------------------------------------------------------------------------------------------------------------------
___________________________________________
3 / ________________________________
70312500000*\/ 18 + I*\/ 272848410531878471374511718426
$$\frac{\left(-1 + 2 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{\sqrt{272848410531878471374511718426}}{18} \right)}}{3} \right)}\right) \left(6103515625 \sqrt[3]{180} + \sqrt[3]{150} \left(18 + \sqrt{272848410531878471374511718426} i\right)^{\frac{2}{3}}\right)}{70312500000 \sqrt[3]{18 + \sqrt{272848410531878471374511718426} i}}$$
(-1 + 2*cos(2*atan(sqrt(272848410531878471374511718426)/18)/3))*(6103515625*180^(1/3) + 150^(1/3)*(18 + i*sqrt(272848410531878471374511718426))^(2/3))/(70312500000*(18 + i*sqrt(272848410531878471374511718426))^(1/3))
Numerical answer
[src]
x1 = 0.031622776601684
x2 = -0.0316227766016836
x3 = -4.194304e-16
x3 = -4.194304e-16