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Expresiones semejantes
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- (1)*(x)^3+4*x^3-5*x+1=0
(-1)*(x)^3+4*x^3-5*x+1=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 3 - x + 4*x - 5*x + 1 = 0
$$\left(- 5 x + \left(- x^{3} + 4 x^{3}\right)\right) + 1 = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(- 5 x + \left(- x^{3} + 4 x^{3}\right)\right) + 1 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - \frac{5 x}{3} + \frac{1}{3} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{5}{3}$$
$$v = \frac{d}{a}$$
$$v = \frac{1}{3}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{5}{3}$$
$$x_{1} x_{2} x_{3} = \frac{1}{3}$$
$$\left(- 5 x + \left(- x^{3} + 4 x^{3}\right)\right) + 1 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - \frac{5 x}{3} + \frac{1}{3} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{5}{3}$$
$$v = \frac{d}{a}$$
$$v = \frac{1}{3}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{5}{3}$$
$$x_{1} x_{2} x_{3} = \frac{1}{3}$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
5*re|------------------------------------| | 5*im|------------------------------------| / / _____\\ / / _____\\| / / _____\\ / / _____\\
| _______________| | | _______________| | |\/ 419 || | |\/ 419 ||| | |\/ 419 || | |\/ 419 ||
|/ ___\ / _____ | | |/ ___\ / _____ | |atan|-------|| |atan|-------||| |atan|-------|| |atan|-------||
|| 1 I*\/ 3 | / 9 I*\/ 419 | | || 1 I*\/ 3 | / 9 I*\/ 419 | ___ | \ 9 /| ____ | \ 9 /|| ____ | \ 9 /| ___ | \ 9 /|
||- - - -------|*3 / - + --------- | | ||- - - -------|*3 / - + --------- | \/ 5 *sin|-------------| \/ 15 *cos|-------------|| \/ 15 *sin|-------------| \/ 5 *cos|-------------|
\\ 2 2 / \/ 2 2 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = - ------------------------------------------ + I*|- ------------------------------------------ + ------------------------ + -------------------------| - ------------------------- + ------------------------
3 \ 3 6 6 / 6 6
$$x_{1} = - \frac{\sqrt{15} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} - \frac{5 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3} + \frac{\sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + i \left(- \frac{5 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3} + \frac{\sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + \frac{\sqrt{15} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6}\right)$$
/ 1 \ / / 1 \ \
5*re|------------------------------------| | 5*im|------------------------------------| / / _____\\ / / _____\\| / / _____\\ / / _____\\
| _______________| | | _______________| | |\/ 419 || | |\/ 419 ||| | |\/ 419 || | |\/ 419 ||
|/ ___\ / _____ | | |/ ___\ / _____ | |atan|-------|| |atan|-------||| |atan|-------|| |atan|-------||
|| 1 I*\/ 3 | / 9 I*\/ 419 | | || 1 I*\/ 3 | / 9 I*\/ 419 | ____ | \ 9 /| ___ | \ 9 /|| ___ | \ 9 /| ____ | \ 9 /|
||- - + -------|*3 / - + --------- | | ||- - + -------|*3 / - + --------- | \/ 15 *cos|-------------| \/ 5 *sin|-------------|| \/ 5 *cos|-------------| \/ 15 *sin|-------------|
\\ 2 2 / \/ 2 2 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = - ------------------------------------------ + I*|- ------------------------------------------ - ------------------------- + ------------------------| + ------------------------ + -------------------------
3 \ 3 6 6 / 6 6
$$x_{2} = \frac{\sqrt{15} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + \frac{\sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} - \frac{5 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3} + i \left(- \frac{\sqrt{15} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + \frac{\sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} - \frac{5 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3}\right)$$
_______________
/ _____
/ 9 I*\/ 419
3 / - + ---------
5 \/ 2 2
x3 = - ---------------------- - --------------------
_______________ 3
/ _____
/ 9 I*\/ 419
3*3 / - + ---------
\/ 2 2
$$x_{3} = - \frac{\sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}{3} - \frac{5}{3 \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}$$
x3 = -(9/2 + sqrt(419)*i/2)^(1/3)/3 - 5/(3*(9/2 + sqrt(419)*i/2)^(1/3))
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
5*re|------------------------------------| | 5*im|------------------------------------| / / _____\\ / / _____\\| / / _____\\ / / _____\\ 5*re|------------------------------------| | 5*im|------------------------------------| / / _____\\ / / _____\\| / / _____\\ / / _____\\
| _______________| | | _______________| | |\/ 419 || | |\/ 419 ||| | |\/ 419 || | |\/ 419 || | _______________| | | _______________| | |\/ 419 || | |\/ 419 ||| | |\/ 419 || | |\/ 419 || _______________
|/ ___\ / _____ | | |/ ___\ / _____ | |atan|-------|| |atan|-------||| |atan|-------|| |atan|-------|| |/ ___\ / _____ | | |/ ___\ / _____ | |atan|-------|| |atan|-------||| |atan|-------|| |atan|-------|| / _____
|| 1 I*\/ 3 | / 9 I*\/ 419 | | || 1 I*\/ 3 | / 9 I*\/ 419 | ___ | \ 9 /| ____ | \ 9 /|| ____ | \ 9 /| ___ | \ 9 /| || 1 I*\/ 3 | / 9 I*\/ 419 | | || 1 I*\/ 3 | / 9 I*\/ 419 | ____ | \ 9 /| ___ | \ 9 /|| ___ | \ 9 /| ____ | \ 9 /| / 9 I*\/ 419
||- - - -------|*3 / - + --------- | | ||- - - -------|*3 / - + --------- | \/ 5 *sin|-------------| \/ 15 *cos|-------------|| \/ 15 *sin|-------------| \/ 5 *cos|-------------| ||- - + -------|*3 / - + --------- | | ||- - + -------|*3 / - + --------- | \/ 15 *cos|-------------| \/ 5 *sin|-------------|| \/ 5 *cos|-------------| \/ 15 *sin|-------------| 3 / - + ---------
\\ 2 2 / \/ 2 2 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 / \ 3 / \\ 2 2 / \/ 2 2 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 / \ 3 / 5 \/ 2 2
- ------------------------------------------ + I*|- ------------------------------------------ + ------------------------ + -------------------------| - ------------------------- + ------------------------ + - ------------------------------------------ + I*|- ------------------------------------------ - ------------------------- + ------------------------| + ------------------------ + ------------------------- + - ---------------------- - --------------------
3 \ 3 6 6 / 6 6 3 \ 3 6 6 / 6 6 _______________ 3
/ _____
/ 9 I*\/ 419
3*3 / - + ---------
\/ 2 2
$$\left(\left(- \frac{\sqrt{15} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} - \frac{5 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3} + \frac{\sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + i \left(- \frac{5 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3} + \frac{\sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + \frac{\sqrt{15} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6}\right)\right) + \left(\frac{\sqrt{15} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + \frac{\sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} - \frac{5 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3} + i \left(- \frac{\sqrt{15} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + \frac{\sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} - \frac{5 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3}\right)\right)\right) + \left(- \frac{\sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}{3} - \frac{5}{3 \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
5*re|------------------------------------| 5*re|------------------------------------| | 5*im|------------------------------------| / / _____\\ / / _____\\| | 5*im|------------------------------------| / / _____\\ / / _____\\| / / _____\\
| _______________| | _______________| _______________ | | _______________| | |\/ 419 || | |\/ 419 ||| | | _______________| | |\/ 419 || | |\/ 419 ||| | |\/ 419 ||
|/ ___\ / _____ | |/ ___\ / _____ | / _____ | |/ ___\ / _____ | |atan|-------|| |atan|-------||| | |/ ___\ / _____ | |atan|-------|| |atan|-------||| |atan|-------||
|| 1 I*\/ 3 | / 9 I*\/ 419 | || 1 I*\/ 3 | / 9 I*\/ 419 | / 9 I*\/ 419 | || 1 I*\/ 3 | / 9 I*\/ 419 | ____ | \ 9 /| ___ | \ 9 /|| | || 1 I*\/ 3 | / 9 I*\/ 419 | ___ | \ 9 /| ____ | \ 9 /|| ___ | \ 9 /|
||- - + -------|*3 / - + --------- | ||- - - -------|*3 / - + --------- | 3 / - + --------- | ||- - + -------|*3 / - + --------- | \/ 15 *cos|-------------| \/ 5 *sin|-------------|| | ||- - - -------|*3 / - + --------- | \/ 5 *sin|-------------| \/ 15 *cos|-------------|| \/ 5 *cos|-------------|
5 \\ 2 2 / \/ 2 2 / \\ 2 2 / \/ 2 2 / \/ 2 2 | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 /
- ---------------------- - ------------------------------------------ - ------------------------------------------ - -------------------- + I*|- ------------------------------------------ - ------------------------- + ------------------------| + I*|- ------------------------------------------ + ------------------------ + -------------------------| + ------------------------
_______________ 3 3 3 \ 3 6 6 / \ 3 6 6 / 3
/ _____
/ 9 I*\/ 419
3*3 / - + ---------
\/ 2 2
$$- \frac{5 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3} - \frac{5 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3} + \frac{\sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{3} - \frac{\sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}{3} + i \left(- \frac{5 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3} + \frac{\sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + \frac{\sqrt{15} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6}\right) + i \left(- \frac{\sqrt{15} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + \frac{\sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} - \frac{5 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3}\right) - \frac{5}{3 \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 5*re|------------------------------------| | 5*im|------------------------------------| / / _____\\ / / _____\\| / / _____\\ / / _____\\| | 5*re|------------------------------------| | 5*im|------------------------------------| / / _____\\ / / _____\\| / / _____\\ / / _____\\|
| | _______________| | | _______________| | |\/ 419 || | |\/ 419 ||| | |\/ 419 || | |\/ 419 ||| | | _______________| | | _______________| | |\/ 419 || | |\/ 419 ||| | |\/ 419 || | |\/ 419 ||| / _______________\
| |/ ___\ / _____ | | |/ ___\ / _____ | |atan|-------|| |atan|-------||| |atan|-------|| |atan|-------||| | |/ ___\ / _____ | | |/ ___\ / _____ | |atan|-------|| |atan|-------||| |atan|-------|| |atan|-------||| | / _____ |
| || 1 I*\/ 3 | / 9 I*\/ 419 | | || 1 I*\/ 3 | / 9 I*\/ 419 | ___ | \ 9 /| ____ | \ 9 /|| ____ | \ 9 /| ___ | \ 9 /|| | || 1 I*\/ 3 | / 9 I*\/ 419 | | || 1 I*\/ 3 | / 9 I*\/ 419 | ____ | \ 9 /| ___ | \ 9 /|| ___ | \ 9 /| ____ | \ 9 /|| | / 9 I*\/ 419 |
| ||- - - -------|*3 / - + --------- | | ||- - - -------|*3 / - + --------- | \/ 5 *sin|-------------| \/ 15 *cos|-------------|| \/ 15 *sin|-------------| \/ 5 *cos|-------------|| | ||- - + -------|*3 / - + --------- | | ||- - + -------|*3 / - + --------- | \/ 15 *cos|-------------| \/ 5 *sin|-------------|| \/ 5 *cos|-------------| \/ 15 *sin|-------------|| | 3 / - + --------- |
| \\ 2 2 / \/ 2 2 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 / \ 3 /| | \\ 2 2 / \/ 2 2 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 / \ 3 /| | 5 \/ 2 2 |
|- ------------------------------------------ + I*|- ------------------------------------------ + ------------------------ + -------------------------| - ------------------------- + ------------------------|*|- ------------------------------------------ + I*|- ------------------------------------------ - ------------------------- + ------------------------| + ------------------------ + -------------------------|*|- ---------------------- - --------------------|
\ 3 \ 3 6 6 / 6 6 / \ 3 \ 3 6 6 / 6 6 / | _______________ 3 |
| / _____ |
| / 9 I*\/ 419 |
| 3*3 / - + --------- |
\ \/ 2 2 /
$$\left(- \frac{\sqrt{15} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} - \frac{5 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3} + \frac{\sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + i \left(- \frac{5 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3} + \frac{\sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + \frac{\sqrt{15} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6}\right)\right) \left(\frac{\sqrt{15} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + \frac{\sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} - \frac{5 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3} + i \left(- \frac{\sqrt{15} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} + \frac{\sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}}{6} - \frac{5 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)}}{3}\right)\right) \left(- \frac{\sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}{3} - \frac{5}{3 \sqrt[3]{\frac{9}{2} + \frac{\sqrt{419} i}{2}}}\right)$$
=
/ / / _____\\\
| | |\/ 419 |||
| |2*atan|-------||| / 2/3\
3 ___ | | \ 9 /|| | 3 ___ / _____\ |
5*\/ 2 *|1 - 2*cos|---------------||*\10 + \/ 2 *\9 + I*\/ 419 / /
\ \ 3 //
--------------------------------------------------------------------
_______________
3 / _____
54*\/ 9 + I*\/ 419
$$\frac{5 \sqrt[3]{2} \left(1 - 2 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{\sqrt{419}}{9} \right)}}{3} \right)}\right) \left(10 + \sqrt[3]{2} \left(9 + \sqrt{419} i\right)^{\frac{2}{3}}\right)}{54 \sqrt[3]{9 + \sqrt{419} i}}$$
5*2^(1/3)*(1 - 2*cos(2*atan(sqrt(419)/9)/3))*(10 + 2^(1/3)*(9 + i*sqrt(419))^(2/3))/(54*(9 + i*sqrt(419))^(1/3))
Respuesta numérica
[src]
x1 = 0.205182924689048
x2 = 1.17611555735495
x3 = -1.38129848204399
x3 = -1.38129848204399