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Ecuación x^4+x^3+x^2+x+1=0
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- Expresar {x} en función de y en la ecuación:
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- Gráfico de la función y =:
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2*x^3+9*x^2-24*x-56
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Expresiones idénticas
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- dos multiplicar por x en el grado tres más nueve multiplicar por x en el grado dos menos veinticuatro multiplicar por x menos cincuenta y seis es igual a cero
- 2*x3+9*x2-24*x-56=0
- 2*x³+9*x²-24*x-56=0
- 2*x en el grado 3+9*x en el grado 2-24*x-56=0
- 2x^3+9x^2-24x-56=0
- 2x3+9x2-24x-56=0
- 2*x^3+9*x^2-24*x-56=O
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Expresiones semejantes
- 2*x^3+9*x^2-24*x+56=0
- 2*x^3+9*x^2+24*x-56=0
- 2*x^3-9*x^2-24*x-56=0
2*x^3+9*x^2-24*x-56=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 2*x + 9*x - 24*x - 56 = 0
$$\left(- 24 x + \left(2 x^{3} + 9 x^{2}\right)\right) - 56 = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(- 24 x + \left(2 x^{3} + 9 x^{2}\right)\right) - 56 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{9 x^{2}}{2} - 12 x - 28 = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{9}{2}$$
$$q = \frac{c}{a}$$
$$q = -12$$
$$v = \frac{d}{a}$$
$$v = -28$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = - \frac{9}{2}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -12$$
$$x_{1} x_{2} x_{3} = -28$$
$$\left(- 24 x + \left(2 x^{3} + 9 x^{2}\right)\right) - 56 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{9 x^{2}}{2} - 12 x - 28 = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{9}{2}$$
$$q = \frac{c}{a}$$
$$q = -12$$
$$v = \frac{d}{a}$$
$$v = -28$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = - \frac{9}{2}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -12$$
$$x_{1} x_{2} x_{3} = -28$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
/ / _____\\ 25*re|-------------------------------------| | / / _____\\ 25*im|-------------------------------------| / / _____\\| / / _____\\
| |4*\/ 966 || | ________________| | | |4*\/ 966 || | ________________| | |4*\/ 966 ||| | |4*\/ 966 ||
|atan|---------|| |/ ___\ / _____ | | |atan|---------|| |/ ___\ / _____ | |atan|---------||| |atan|---------||
| \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | | | \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | ___ | \ 13 /|| ___ | \ 13 /|
5*cos|---------------| ||- - - -------|*3 / -- + --------- | | 5*sin|---------------| ||- - - -------|*3 / -- + --------- | 5*\/ 3 *cos|---------------|| 5*\/ 3 *sin|---------------|
3 \ 3 / \\ 2 2 / \/ 8 2 / | \ 3 / \\ 2 2 / \/ 8 2 / \ 3 /| \ 3 /
x1 = - - - ---------------------- + -------------------------------------------- + I*|- ---------------------- + -------------------------------------------- - ----------------------------| + ----------------------------
2 4 4 \ 4 4 4 / 4
$$x_{1} = - \frac{3}{2} - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + \frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4} + \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + i \left(- \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + \frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4}\right)$$
/ 1 \ / / 1 \ \
/ / _____\\ 25*re|-------------------------------------| | / / _____\\ 25*im|-------------------------------------| / / _____\\| / / _____\\
| |4*\/ 966 || | ________________| | | |4*\/ 966 || | ________________| | |4*\/ 966 ||| | |4*\/ 966 ||
|atan|---------|| |/ ___\ / _____ | | |atan|---------|| |/ ___\ / _____ | |atan|---------||| |atan|---------||
| \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | | | \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | ___ | \ 13 /|| ___ | \ 13 /|
5*cos|---------------| ||- - + -------|*3 / -- + --------- | | 5*sin|---------------| ||- - + -------|*3 / -- + --------- | 5*\/ 3 *cos|---------------|| 5*\/ 3 *sin|---------------|
3 \ 3 / \\ 2 2 / \/ 8 2 / | \ 3 / \\ 2 2 / \/ 8 2 / \ 3 /| \ 3 /
x2 = - - - ---------------------- + -------------------------------------------- + I*|- ---------------------- + -------------------------------------------- + ----------------------------| - ----------------------------
2 4 4 \ 4 4 4 / 4
$$x_{2} = \frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4} - \frac{3}{2} - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} - \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + i \left(\frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4}\right)$$
________________
/ _____
3 / 13 I*\/ 966 25
x3 = - - + 3 / -- + --------- + -----------------------
2 \/ 8 2 ________________
/ _____
/ 13 I*\/ 966
4*3 / -- + ---------
\/ 8 2
$$x_{3} = - \frac{3}{2} + \frac{25}{4 \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}} + \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}$$
x3 = -3/2 + 25/(4*(13/8 + sqrt(966)*i/2)^(1/3)) + (13/8 + sqrt(966)*i/2)^(1/3)
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
/ / _____\\ 25*re|-------------------------------------| | / / _____\\ 25*im|-------------------------------------| / / _____\\| / / _____\\ / / _____\\ 25*re|-------------------------------------| | / / _____\\ 25*im|-------------------------------------| / / _____\\| / / _____\\
| |4*\/ 966 || | ________________| | | |4*\/ 966 || | ________________| | |4*\/ 966 ||| | |4*\/ 966 || | |4*\/ 966 || | ________________| | | |4*\/ 966 || | ________________| | |4*\/ 966 ||| | |4*\/ 966 ||
|atan|---------|| |/ ___\ / _____ | | |atan|---------|| |/ ___\ / _____ | |atan|---------||| |atan|---------|| |atan|---------|| |/ ___\ / _____ | | |atan|---------|| |/ ___\ / _____ | |atan|---------||| |atan|---------||
| \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | | | \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | ___ | \ 13 /|| ___ | \ 13 /| | \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | | | \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | ___ | \ 13 /|| ___ | \ 13 /| ________________
5*cos|---------------| ||- - - -------|*3 / -- + --------- | | 5*sin|---------------| ||- - - -------|*3 / -- + --------- | 5*\/ 3 *cos|---------------|| 5*\/ 3 *sin|---------------| 5*cos|---------------| ||- - + -------|*3 / -- + --------- | | 5*sin|---------------| ||- - + -------|*3 / -- + --------- | 5*\/ 3 *cos|---------------|| 5*\/ 3 *sin|---------------| / _____
3 \ 3 / \\ 2 2 / \/ 8 2 / | \ 3 / \\ 2 2 / \/ 8 2 / \ 3 /| \ 3 / 3 \ 3 / \\ 2 2 / \/ 8 2 / | \ 3 / \\ 2 2 / \/ 8 2 / \ 3 /| \ 3 / 3 / 13 I*\/ 966 25
- - - ---------------------- + -------------------------------------------- + I*|- ---------------------- + -------------------------------------------- - ----------------------------| + ---------------------------- + - - - ---------------------- + -------------------------------------------- + I*|- ---------------------- + -------------------------------------------- + ----------------------------| - ---------------------------- + - - + 3 / -- + --------- + -----------------------
2 4 4 \ 4 4 4 / 4 2 4 4 \ 4 4 4 / 4 2 \/ 8 2 ________________
/ _____
/ 13 I*\/ 966
4*3 / -- + ---------
\/ 8 2
$$\left(- \frac{3}{2} + \frac{25}{4 \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}} + \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}\right) + \left(\left(- \frac{3}{2} - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + \frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4} + \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + i \left(- \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + \frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4}\right)\right) + \left(\frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4} - \frac{3}{2} - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} - \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + i \left(\frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4}\right)\right)\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
/ / _____\\ 25*re|-------------------------------------| 25*re|-------------------------------------| | / / _____\\ 25*im|-------------------------------------| / / _____\\| | / / _____\\ 25*im|-------------------------------------| / / _____\\|
| |4*\/ 966 || | ________________| | ________________| | | |4*\/ 966 || | ________________| | |4*\/ 966 ||| | | |4*\/ 966 || | ________________| | |4*\/ 966 |||
|atan|---------|| |/ ___\ / _____ | |/ ___\ / _____ | | |atan|---------|| |/ ___\ / _____ | |atan|---------||| | |atan|---------|| |/ ___\ / _____ | |atan|---------|||
________________ | \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | || 1 I*\/ 3 | / 13 I*\/ 966 | | | \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | ___ | \ 13 /|| | | \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | ___ | \ 13 /||
/ _____ 5*cos|---------------| ||- - + -------|*3 / -- + --------- | ||- - - -------|*3 / -- + --------- | | 5*sin|---------------| ||- - + -------|*3 / -- + --------- | 5*\/ 3 *cos|---------------|| | 5*sin|---------------| ||- - - -------|*3 / -- + --------- | 5*\/ 3 *cos|---------------||
9 / 13 I*\/ 966 \ 3 / 25 \\ 2 2 / \/ 8 2 / \\ 2 2 / \/ 8 2 / | \ 3 / \\ 2 2 / \/ 8 2 / \ 3 /| | \ 3 / \\ 2 2 / \/ 8 2 / \ 3 /|
- - + 3 / -- + --------- - ---------------------- + ----------------------- + -------------------------------------------- + -------------------------------------------- + I*|- ---------------------- + -------------------------------------------- + ----------------------------| + I*|- ---------------------- + -------------------------------------------- - ----------------------------|
2 \/ 8 2 2 ________________ 4 4 \ 4 4 4 / \ 4 4 4 /
/ _____
/ 13 I*\/ 966
4*3 / -- + ---------
\/ 8 2
$$- \frac{9}{2} - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{2} + \frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4} + \frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4} + \frac{25}{4 \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}} + i \left(- \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + \frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4}\right) + i \left(\frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4}\right) + \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| / / _____\\ 25*re|-------------------------------------| | / / _____\\ 25*im|-------------------------------------| / / _____\\| / / _____\\| | / / _____\\ 25*re|-------------------------------------| | / / _____\\ 25*im|-------------------------------------| / / _____\\| / / _____\\|
| | |4*\/ 966 || | ________________| | | |4*\/ 966 || | ________________| | |4*\/ 966 ||| | |4*\/ 966 ||| | | |4*\/ 966 || | ________________| | | |4*\/ 966 || | ________________| | |4*\/ 966 ||| | |4*\/ 966 |||
| |atan|---------|| |/ ___\ / _____ | | |atan|---------|| |/ ___\ / _____ | |atan|---------||| |atan|---------||| | |atan|---------|| |/ ___\ / _____ | | |atan|---------|| |/ ___\ / _____ | |atan|---------||| |atan|---------|||
| | \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | | | \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | ___ | \ 13 /|| ___ | \ 13 /|| | | \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | | | \ 13 /| || 1 I*\/ 3 | / 13 I*\/ 966 | ___ | \ 13 /|| ___ | \ 13 /|| / ________________ \
| 5*cos|---------------| ||- - - -------|*3 / -- + --------- | | 5*sin|---------------| ||- - - -------|*3 / -- + --------- | 5*\/ 3 *cos|---------------|| 5*\/ 3 *sin|---------------|| | 5*cos|---------------| ||- - + -------|*3 / -- + --------- | | 5*sin|---------------| ||- - + -------|*3 / -- + --------- | 5*\/ 3 *cos|---------------|| 5*\/ 3 *sin|---------------|| | / _____ |
| 3 \ 3 / \\ 2 2 / \/ 8 2 / | \ 3 / \\ 2 2 / \/ 8 2 / \ 3 /| \ 3 /| | 3 \ 3 / \\ 2 2 / \/ 8 2 / | \ 3 / \\ 2 2 / \/ 8 2 / \ 3 /| \ 3 /| | 3 / 13 I*\/ 966 25 |
|- - - ---------------------- + -------------------------------------------- + I*|- ---------------------- + -------------------------------------------- - ----------------------------| + ----------------------------|*|- - - ---------------------- + -------------------------------------------- + I*|- ---------------------- + -------------------------------------------- + ----------------------------| - ----------------------------|*|- - + 3 / -- + --------- + -----------------------|
\ 2 4 4 \ 4 4 4 / 4 / \ 2 4 4 \ 4 4 4 / 4 / | 2 \/ 8 2 ________________|
| / _____ |
| / 13 I*\/ 966 |
| 4*3 / -- + --------- |
\ \/ 8 2 /
$$\left(- \frac{3}{2} - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + \frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4} + \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + i \left(- \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + \frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4}\right)\right) \left(\frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4} - \frac{3}{2} - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} - \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + i \left(\frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}}\right)}}{4} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4} + \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}}{4}\right)\right) \left(- \frac{3}{2} + \frac{25}{4 \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}} + \sqrt[3]{\frac{13}{8} + \frac{\sqrt{966} i}{2}}\right)$$
=
/ / / _____\\ / / _____\\\
| | |4*\/ 966 || | |4*\/ 966 |||
/ __________________ / __________________\\ | |atan|---------|| |2*atan|---------|||
| 3 / _____ | 3 / _____ || | | \ 13 /| | \ 13 /||
\25 + \/ 13 + 4*I*\/ 966 *\-3 + \/ 13 + 4*I*\/ 966 //*|-64 + 120*cos|---------------| + 200*cos|-----------------||
\ \ 3 / \ 3 //
-----------------------------------------------------------------------------------------------------------------------
__________________
3 / _____
32*\/ 13 + 4*I*\/ 966
$$\frac{\left(25 + \left(-3 + \sqrt[3]{13 + 4 \sqrt{966} i}\right) \sqrt[3]{13 + 4 \sqrt{966} i}\right) \left(-64 + 120 \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)} + 200 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{4 \sqrt{966}}{13} \right)}}{3} \right)}\right)}{32 \sqrt[3]{13 + 4 \sqrt{966} i}}$$
(25 + (13 + 4*i*sqrt(966))^(1/3)*(-3 + (13 + 4*i*sqrt(966))^(1/3)))*(-64 + 120*cos(atan(4*sqrt(966)/13)/3) + 200*cos(2*atan(4*sqrt(966)/13)/3))/(32*(13 + 4*i*sqrt(966))^(1/3))
Respuesta numérica
[src]
x1 = -1.67361242129904
x2 = -5.74070971021987
x3 = 2.9143221315189
x3 = 2.9143221315189