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- menos x al cubo menos x al cuadrado más 161 multiplicar por x menos 80 es igual a 0
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Expresiones semejantes
- -x^3-x^2+161*x+80=0
- x^3-x^2+161*x-80=0
- -x^3+x^2+161*x-80=0
- -x^3-x^2-161*x-80=0
-x^3-x^2+161*x-80=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 - x - x + 161*x - 80 = 0
$$\left(161 x + \left(- x^{3} - x^{2}\right)\right) - 80 = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(161 x + \left(- x^{3} - x^{2}\right)\right) - 80 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + x^{2} - 161 x + 80 = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = -161$$
$$v = \frac{d}{a}$$
$$v = 80$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -1$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -161$$
$$x_{1} x_{2} x_{3} = 80$$
$$\left(161 x + \left(- x^{3} - x^{2}\right)\right) - 80 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + x^{2} - 161 x + 80 = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = -161$$
$$v = \frac{d}{a}$$
$$v = 80$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -1$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -161$$
$$x_{1} x_{2} x_{3} = 80$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
484*re|----------------------------------------------| / / __________\\ | 484*im|----------------------------------------------| / / __________\\ / / __________\\| / / __________\\
| _________________________| | |3*\/ 48942255 || | | _________________________| | |3*\/ 48942255 || | |3*\/ 48942255 ||| | |3*\/ 48942255 ||
|/ ___\ / __________ | |atan|--------------|| | |/ ___\ / __________ | |atan|--------------|| |atan|--------------||| |atan|--------------||
|| 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| | || 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| ___ | \ 3611 /|| ___ | \ 3611 /|
||- - - -------|*3 / ---- + ---------------- | 11*cos|--------------------| | ||- - - -------|*3 / ---- + ---------------- | 11*sin|--------------------| 11*\/ 3 *cos|--------------------|| 11*\/ 3 *sin|--------------------|
1 \\ 2 2 / \/ 2 2 / \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 /
x1 = - - - ------------------------------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- + ----------------------------------| - ----------------------------------
3 3 3 \ 3 3 3 / 3
$$x_{1} = - \frac{11 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{1}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + i \left(- \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3}\right)$$
/ 1 \ / / 1 \ \
484*re|----------------------------------------------| / / __________\\ | 484*im|----------------------------------------------| / / __________\\ / / __________\\| / / __________\\
| _________________________| | |3*\/ 48942255 || | | _________________________| | |3*\/ 48942255 || | |3*\/ 48942255 ||| | |3*\/ 48942255 ||
|/ ___\ / __________ | |atan|--------------|| | |/ ___\ / __________ | |atan|--------------|| |atan|--------------||| |atan|--------------||
|| 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| | || 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| ___ | \ 3611 /|| ___ | \ 3611 /|
||- - + -------|*3 / ---- + ---------------- | 11*cos|--------------------| | ||- - + -------|*3 / ---- + ---------------- | 11*sin|--------------------| 11*\/ 3 *cos|--------------------|| 11*\/ 3 *sin|--------------------|
1 \\ 2 2 / \/ 2 2 / \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 /
x2 = - - - ------------------------------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- - ----------------------------------| + ----------------------------------
3 3 3 \ 3 3 3 / 3
$$x_{2} = - \frac{1}{3} + \frac{11 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + i \left(- \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3}\right)$$
_________________________
/ __________
/ 3611 3*I*\/ 48942255
3 / ---- + ----------------
1 484 \/ 2 2
x3 = - - - -------------------------------- - ------------------------------
3 _________________________ 3
/ __________
/ 3611 3*I*\/ 48942255
3*3 / ---- + ----------------
\/ 2 2
$$x_{3} = - \frac{1}{3} - \frac{\sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}{3} - \frac{484}{3 \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}$$
x3 = -1/3 - (3611/2 + 3*sqrt(48942255)*i/2)^(1/3)/3 - 484/(3*(3611/2 + 3*sqrt(48942255)*i/2)^(1/3))
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
484*re|----------------------------------------------| / / __________\\ | 484*im|----------------------------------------------| / / __________\\ / / __________\\| / / __________\\ 484*re|----------------------------------------------| / / __________\\ | 484*im|----------------------------------------------| / / __________\\ / / __________\\| / / __________\\
| _________________________| | |3*\/ 48942255 || | | _________________________| | |3*\/ 48942255 || | |3*\/ 48942255 ||| | |3*\/ 48942255 || | _________________________| | |3*\/ 48942255 || | | _________________________| | |3*\/ 48942255 || | |3*\/ 48942255 ||| | |3*\/ 48942255 || _________________________
|/ ___\ / __________ | |atan|--------------|| | |/ ___\ / __________ | |atan|--------------|| |atan|--------------||| |atan|--------------|| |/ ___\ / __________ | |atan|--------------|| | |/ ___\ / __________ | |atan|--------------|| |atan|--------------||| |atan|--------------|| / __________
|| 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| | || 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| ___ | \ 3611 /|| ___ | \ 3611 /| || 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| | || 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| ___ | \ 3611 /|| ___ | \ 3611 /| / 3611 3*I*\/ 48942255
||- - - -------|*3 / ---- + ---------------- | 11*cos|--------------------| | ||- - - -------|*3 / ---- + ---------------- | 11*sin|--------------------| 11*\/ 3 *cos|--------------------|| 11*\/ 3 *sin|--------------------| ||- - + -------|*3 / ---- + ---------------- | 11*cos|--------------------| | ||- - + -------|*3 / ---- + ---------------- | 11*sin|--------------------| 11*\/ 3 *cos|--------------------|| 11*\/ 3 *sin|--------------------| 3 / ---- + ----------------
1 \\ 2 2 / \/ 2 2 / \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 / 1 \\ 2 2 / \/ 2 2 / \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 / 1 484 \/ 2 2
- - - ------------------------------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- + ----------------------------------| - ---------------------------------- + - - - ------------------------------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- - ----------------------------------| + ---------------------------------- + - - - -------------------------------- - ------------------------------
3 3 3 \ 3 3 3 / 3 3 3 3 \ 3 3 3 / 3 3 _________________________ 3
/ __________
/ 3611 3*I*\/ 48942255
3*3 / ---- + ----------------
\/ 2 2
$$\left(\left(- \frac{11 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{1}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + i \left(- \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3}\right)\right) + \left(- \frac{1}{3} + \frac{11 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + i \left(- \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3}\right)\right)\right) + \left(- \frac{1}{3} - \frac{\sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}{3} - \frac{484}{3 \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
484*re|----------------------------------------------| 484*re|----------------------------------------------| / / __________\\ | 484*im|----------------------------------------------| / / __________\\ / / __________\\| | 484*im|----------------------------------------------| / / __________\\ / / __________\\|
| _________________________| | _________________________| _________________________ | |3*\/ 48942255 || | | _________________________| | |3*\/ 48942255 || | |3*\/ 48942255 ||| | | _________________________| | |3*\/ 48942255 || | |3*\/ 48942255 |||
|/ ___\ / __________ | |/ ___\ / __________ | / __________ |atan|--------------|| | |/ ___\ / __________ | |atan|--------------|| |atan|--------------||| | |/ ___\ / __________ | |atan|--------------|| |atan|--------------|||
|| 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | || 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | / 3611 3*I*\/ 48942255 | \ 3611 /| | || 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| ___ | \ 3611 /|| | || 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| ___ | \ 3611 /||
||- - + -------|*3 / ---- + ---------------- | ||- - - -------|*3 / ---- + ---------------- | 3 / ---- + ---------------- 22*cos|--------------------| | ||- - + -------|*3 / ---- + ---------------- | 11*sin|--------------------| 11*\/ 3 *cos|--------------------|| | ||- - - -------|*3 / ---- + ---------------- | 11*sin|--------------------| 11*\/ 3 *cos|--------------------||
484 \\ 2 2 / \/ 2 2 / \\ 2 2 / \/ 2 2 / \/ 2 2 \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /|
-1 - -------------------------------- - ------------------------------------------------------ - ------------------------------------------------------ - ------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- - ----------------------------------| + I*|- ------------------------------------------------------ + ---------------------------- + ----------------------------------|
_________________________ 3 3 3 3 \ 3 3 3 / \ 3 3 3 /
/ __________
/ 3611 3*I*\/ 48942255
3*3 / ---- + ----------------
\/ 2 2
$$-1 - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{22 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{\sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}{3} + i \left(- \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3}\right) + i \left(- \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3}\right) - \frac{484}{3 \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 484*re|----------------------------------------------| / / __________\\ | 484*im|----------------------------------------------| / / __________\\ / / __________\\| / / __________\\| | 484*re|----------------------------------------------| / / __________\\ | 484*im|----------------------------------------------| / / __________\\ / / __________\\| / / __________\\|
| | _________________________| | |3*\/ 48942255 || | | _________________________| | |3*\/ 48942255 || | |3*\/ 48942255 ||| | |3*\/ 48942255 ||| | | _________________________| | |3*\/ 48942255 || | | _________________________| | |3*\/ 48942255 || | |3*\/ 48942255 ||| | |3*\/ 48942255 ||| / _________________________\
| |/ ___\ / __________ | |atan|--------------|| | |/ ___\ / __________ | |atan|--------------|| |atan|--------------||| |atan|--------------||| | |/ ___\ / __________ | |atan|--------------|| | |/ ___\ / __________ | |atan|--------------|| |atan|--------------||| |atan|--------------||| | / __________ |
| || 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| | || 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| ___ | \ 3611 /|| ___ | \ 3611 /|| | || 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| | || 1 I*\/ 3 | / 3611 3*I*\/ 48942255 | | \ 3611 /| ___ | \ 3611 /|| ___ | \ 3611 /|| | / 3611 3*I*\/ 48942255 |
| ||- - - -------|*3 / ---- + ---------------- | 11*cos|--------------------| | ||- - - -------|*3 / ---- + ---------------- | 11*sin|--------------------| 11*\/ 3 *cos|--------------------|| 11*\/ 3 *sin|--------------------|| | ||- - + -------|*3 / ---- + ---------------- | 11*cos|--------------------| | ||- - + -------|*3 / ---- + ---------------- | 11*sin|--------------------| 11*\/ 3 *cos|--------------------|| 11*\/ 3 *sin|--------------------|| | 3 / ---- + ---------------- |
| 1 \\ 2 2 / \/ 2 2 / \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 /| | 1 \\ 2 2 / \/ 2 2 / \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 /| | 1 484 \/ 2 2 |
|- - - ------------------------------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- + ----------------------------------| - ----------------------------------|*|- - - ------------------------------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- - ----------------------------------| + ----------------------------------|*|- - - -------------------------------- - ------------------------------|
\ 3 3 3 \ 3 3 3 / 3 / \ 3 3 3 \ 3 3 3 / 3 / | 3 _________________________ 3 |
| / __________ |
| / 3611 3*I*\/ 48942255 |
| 3*3 / ---- + ---------------- |
\ \/ 2 2 /
$$\left(- \frac{1}{3} + \frac{11 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + i \left(- \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3}\right)\right) \left(- \frac{11 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{1}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + i \left(- \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3}\right)\right) \left(- \frac{1}{3} - \frac{\sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}{3} - \frac{484}{3 \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)$$
=
/ / / __________\\ / / __________\\\
| | |3*\/ 48942255 || | |3*\/ 48942255 |||
/ _________________________ / _________________________\\ | |2*atan|--------------|| |atan|--------------|||
| 3 ___ 3 / __________ | 2/3 3 / __________ || | | \ 3611 /| | \ 3611 /||
\968*\/ 2 + \/ 3611 + 3*I*\/ 48942255 *\2 + 2 *\/ 3611 + 3*I*\/ 48942255 //*|483 - 968*cos|----------------------| + 44*cos|--------------------||
\ \ 3 / \ 3 //
---------------------------------------------------------------------------------------------------------------------------------------------------------
_________________________
3 / __________
54*\/ 3611 + 3*I*\/ 48942255
$$\frac{\left(968 \sqrt[3]{2} + \left(2 + 2^{\frac{2}{3}} \sqrt[3]{3611 + 3 \sqrt{48942255} i}\right) \sqrt[3]{3611 + 3 \sqrt{48942255} i}\right) \left(- 968 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)} + 44 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)} + 483\right)}{54 \sqrt[3]{3611 + 3 \sqrt{48942255} i}}$$
(968*2^(1/3) + (3611 + 3*i*sqrt(48942255))^(1/3)*(2 + 2^(2/3)*(3611 + 3*i*sqrt(48942255))^(1/3)))*(483 - 968*cos(2*atan(3*sqrt(48942255)/3611)/3) + 44*cos(atan(3*sqrt(48942255)/3611)/3))/(54*(3611 + 3*i*sqrt(48942255))^(1/3))
Respuesta numérica
[src]
x1 = 11.9316179797821
x2 = 0.499215080312488
x3 = -13.4308330600946
x3 = -13.4308330600946