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Expresiones idénticas
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- 1 multiplicar por x al cubo más 418 multiplicar por x al cuadrado menos 418 al cuadrado x menos (418 al cubo menos 17242.3) es igual a 0
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Expresiones semejantes
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1*x^3+418*x^2-418^2x-(418^3-17242.3)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 172423
x + 418*x - 174724*x + -73034632 + ------ = 0
10
$$\left(- 174724 x + \left(x^{3} + 418 x^{2}\right)\right) + \left(-73034632 + \frac{172423}{10}\right) = 0$$
Teorema de Cardano-Vieta
es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 418$$
$$q = \frac{c}{a}$$
$$q = -174724$$
$$v = \frac{d}{a}$$
$$v = -73034632 + \frac{172423}{10}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -418$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -174724$$
$$x_{1} x_{2} x_{3} = -73034632 + \frac{172423}{10}$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 418$$
$$q = \frac{c}{a}$$
$$q = -174724$$
$$v = \frac{d}{a}$$
$$v = -73034632 + \frac{172423}{10}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -418$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -174724$$
$$x_{1} x_{2} x_{3} = -73034632 + \frac{172423}{10}$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
/ / ___________________\\ 698896*re|------------------------------------------------------------| | / / ___________________\\ 698896*im|------------------------------------------------------------| / / ___________________\\| / / ___________________\\
| |3*\/ 12086728234237311 || | _______________________________________| | | |3*\/ 12086728234237311 || | _______________________________________| | |3*\/ 12086728234237311 ||| | |3*\/ 12086728234237311 ||
|atan|-----------------------|| |/ ___\ / ___________________ | | |atan|-----------------------|| |/ ___\ / ___________________ | |atan|-----------------------||| |atan|-----------------------||
| \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | | | \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | ___ | \ 11680885699 /|| ___ | \ 11680885699 /|
418*cos|-----------------------------| ||- - - -------|*3 / ----------- + ----------------------- | | 418*sin|-----------------------------| ||- - - -------|*3 / ----------- + ----------------------- | 418*\/ 3 *cos|-----------------------------|| 418*\/ 3 *sin|-----------------------------|
418 \ 3 / \\ 2 2 / \/ 540 180 / | \ 3 / \\ 2 2 / \/ 540 180 / \ 3 /| \ 3 /
x1 = - --- - -------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- - --------------------------------------------| + --------------------------------------------
3 3 9 \ 3 9 3 / 3
$$x_{1} = - \frac{418}{3} - \frac{418 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} + \frac{418 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + i \left(- \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9}\right)$$
/ 1 \ / / 1 \ \
/ / ___________________\\ 698896*re|------------------------------------------------------------| | / / ___________________\\ 698896*im|------------------------------------------------------------| / / ___________________\\| / / ___________________\\
| |3*\/ 12086728234237311 || | _______________________________________| | | |3*\/ 12086728234237311 || | _______________________________________| | |3*\/ 12086728234237311 ||| | |3*\/ 12086728234237311 ||
|atan|-----------------------|| |/ ___\ / ___________________ | | |atan|-----------------------|| |/ ___\ / ___________________ | |atan|-----------------------||| |atan|-----------------------||
| \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | | | \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | ___ | \ 11680885699 /|| ___ | \ 11680885699 /|
418*cos|-----------------------------| ||- - + -------|*3 / ----------- + ----------------------- | | 418*sin|-----------------------------| ||- - + -------|*3 / ----------- + ----------------------- | 418*\/ 3 *cos|-----------------------------|| 418*\/ 3 *sin|-----------------------------|
418 \ 3 / \\ 2 2 / \/ 540 180 / | \ 3 / \\ 2 2 / \/ 540 180 / \ 3 /| \ 3 /
x2 = - --- - -------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- + --------------------------------------------| - --------------------------------------------
3 3 9 \ 3 9 3 / 3
$$x_{2} = \frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418}{3} - \frac{418 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + i \left(\frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3}\right)$$
_______________________________________
/ ___________________
418 / 11680885699 I*\/ 12086728234237311 698896
x3 = - --- + 3 / ----------- + ----------------------- + ----------------------------------------------
3 \/ 540 180 _______________________________________
/ ___________________
/ 11680885699 I*\/ 12086728234237311
9*3 / ----------- + -----------------------
\/ 540 180
$$x_{3} = - \frac{418}{3} + \frac{698896}{9 \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}} + \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}$$
x3 = -418/3 + 698896/(9*(11680885699/540 + sqrt(12086728234237311)*i/180)^(1/3)) + (11680885699/540 + sqrt(12086728234237311)*i/180)^(1/3)
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
/ / ___________________\\ 698896*re|------------------------------------------------------------| | / / ___________________\\ 698896*im|------------------------------------------------------------| / / ___________________\\| / / ___________________\\ / / ___________________\\ 698896*re|------------------------------------------------------------| | / / ___________________\\ 698896*im|------------------------------------------------------------| / / ___________________\\| / / ___________________\\
| |3*\/ 12086728234237311 || | _______________________________________| | | |3*\/ 12086728234237311 || | _______________________________________| | |3*\/ 12086728234237311 ||| | |3*\/ 12086728234237311 || | |3*\/ 12086728234237311 || | _______________________________________| | | |3*\/ 12086728234237311 || | _______________________________________| | |3*\/ 12086728234237311 ||| | |3*\/ 12086728234237311 ||
|atan|-----------------------|| |/ ___\ / ___________________ | | |atan|-----------------------|| |/ ___\ / ___________________ | |atan|-----------------------||| |atan|-----------------------|| |atan|-----------------------|| |/ ___\ / ___________________ | | |atan|-----------------------|| |/ ___\ / ___________________ | |atan|-----------------------||| |atan|-----------------------||
| \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | | | \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | ___ | \ 11680885699 /|| ___ | \ 11680885699 /| | \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | | | \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | ___ | \ 11680885699 /|| ___ | \ 11680885699 /| _______________________________________
418*cos|-----------------------------| ||- - - -------|*3 / ----------- + ----------------------- | | 418*sin|-----------------------------| ||- - - -------|*3 / ----------- + ----------------------- | 418*\/ 3 *cos|-----------------------------|| 418*\/ 3 *sin|-----------------------------| 418*cos|-----------------------------| ||- - + -------|*3 / ----------- + ----------------------- | | 418*sin|-----------------------------| ||- - + -------|*3 / ----------- + ----------------------- | 418*\/ 3 *cos|-----------------------------|| 418*\/ 3 *sin|-----------------------------| / ___________________
418 \ 3 / \\ 2 2 / \/ 540 180 / | \ 3 / \\ 2 2 / \/ 540 180 / \ 3 /| \ 3 / 418 \ 3 / \\ 2 2 / \/ 540 180 / | \ 3 / \\ 2 2 / \/ 540 180 / \ 3 /| \ 3 / 418 / 11680885699 I*\/ 12086728234237311 698896
- --- - -------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- - --------------------------------------------| + -------------------------------------------- + - --- - -------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- + --------------------------------------------| - -------------------------------------------- + - --- + 3 / ----------- + ----------------------- + ----------------------------------------------
3 3 9 \ 3 9 3 / 3 3 3 9 \ 3 9 3 / 3 3 \/ 540 180 _______________________________________
/ ___________________
/ 11680885699 I*\/ 12086728234237311
9*3 / ----------- + -----------------------
\/ 540 180
$$\left(- \frac{418}{3} + \frac{698896}{9 \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}} + \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}\right) + \left(\left(\frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418}{3} - \frac{418 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + i \left(\frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3}\right)\right) + \left(- \frac{418}{3} - \frac{418 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} + \frac{418 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + i \left(- \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9}\right)\right)\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
/ / ___________________\\ 698896*re|------------------------------------------------------------| 698896*re|------------------------------------------------------------| | / / ___________________\\ 698896*im|------------------------------------------------------------| / / ___________________\\| | / / ___________________\\ 698896*im|------------------------------------------------------------| / / ___________________\\|
| |3*\/ 12086728234237311 || | _______________________________________| | _______________________________________| | | |3*\/ 12086728234237311 || | _______________________________________| | |3*\/ 12086728234237311 ||| | | |3*\/ 12086728234237311 || | _______________________________________| | |3*\/ 12086728234237311 |||
|atan|-----------------------|| |/ ___\ / ___________________ | |/ ___\ / ___________________ | | |atan|-----------------------|| |/ ___\ / ___________________ | |atan|-----------------------||| | |atan|-----------------------|| |/ ___\ / ___________________ | |atan|-----------------------|||
_______________________________________ | \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | | | \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | ___ | \ 11680885699 /|| | | \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | ___ | \ 11680885699 /||
/ ___________________ 836*cos|-----------------------------| ||- - + -------|*3 / ----------- + ----------------------- | ||- - - -------|*3 / ----------- + ----------------------- | | 418*sin|-----------------------------| ||- - + -------|*3 / ----------- + ----------------------- | 418*\/ 3 *cos|-----------------------------|| | 418*sin|-----------------------------| ||- - - -------|*3 / ----------- + ----------------------- | 418*\/ 3 *cos|-----------------------------||
/ 11680885699 I*\/ 12086728234237311 \ 3 / 698896 \\ 2 2 / \/ 540 180 / \\ 2 2 / \/ 540 180 / | \ 3 / \\ 2 2 / \/ 540 180 / \ 3 /| | \ 3 / \\ 2 2 / \/ 540 180 / \ 3 /|
-418 + 3 / ----------- + ----------------------- - -------------------------------------- + ---------------------------------------------- + ----------------------------------------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- + --------------------------------------------| + I*|- -------------------------------------- + ----------------------------------------------------------------------- - --------------------------------------------|
\/ 540 180 3 _______________________________________ 9 9 \ 3 9 3 / \ 3 9 3 /
/ ___________________
/ 11680885699 I*\/ 12086728234237311
9*3 / ----------- + -----------------------
\/ 540 180
$$-418 - \frac{836 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} + \frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} + \frac{698896}{9 \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}} + i \left(\frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3}\right) + i \left(- \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9}\right) + \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| / / ___________________\\ 698896*re|------------------------------------------------------------| | / / ___________________\\ 698896*im|------------------------------------------------------------| / / ___________________\\| / / ___________________\\| | / / ___________________\\ 698896*re|------------------------------------------------------------| | / / ___________________\\ 698896*im|------------------------------------------------------------| / / ___________________\\| / / ___________________\\|
| | |3*\/ 12086728234237311 || | _______________________________________| | | |3*\/ 12086728234237311 || | _______________________________________| | |3*\/ 12086728234237311 ||| | |3*\/ 12086728234237311 ||| | | |3*\/ 12086728234237311 || | _______________________________________| | | |3*\/ 12086728234237311 || | _______________________________________| | |3*\/ 12086728234237311 ||| | |3*\/ 12086728234237311 |||
| |atan|-----------------------|| |/ ___\ / ___________________ | | |atan|-----------------------|| |/ ___\ / ___________________ | |atan|-----------------------||| |atan|-----------------------||| | |atan|-----------------------|| |/ ___\ / ___________________ | | |atan|-----------------------|| |/ ___\ / ___________________ | |atan|-----------------------||| |atan|-----------------------|||
| | \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | | | \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | ___ | \ 11680885699 /|| ___ | \ 11680885699 /|| | | \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | | | \ 11680885699 /| || 1 I*\/ 3 | / 11680885699 I*\/ 12086728234237311 | ___ | \ 11680885699 /|| ___ | \ 11680885699 /|| / _______________________________________ \
| 418*cos|-----------------------------| ||- - - -------|*3 / ----------- + ----------------------- | | 418*sin|-----------------------------| ||- - - -------|*3 / ----------- + ----------------------- | 418*\/ 3 *cos|-----------------------------|| 418*\/ 3 *sin|-----------------------------|| | 418*cos|-----------------------------| ||- - + -------|*3 / ----------- + ----------------------- | | 418*sin|-----------------------------| ||- - + -------|*3 / ----------- + ----------------------- | 418*\/ 3 *cos|-----------------------------|| 418*\/ 3 *sin|-----------------------------|| | / ___________________ |
| 418 \ 3 / \\ 2 2 / \/ 540 180 / | \ 3 / \\ 2 2 / \/ 540 180 / \ 3 /| \ 3 /| | 418 \ 3 / \\ 2 2 / \/ 540 180 / | \ 3 / \\ 2 2 / \/ 540 180 / \ 3 /| \ 3 /| | 418 / 11680885699 I*\/ 12086728234237311 698896 |
|- --- - -------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- - --------------------------------------------| + --------------------------------------------|*|- --- - -------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- + --------------------------------------------| - --------------------------------------------|*|- --- + 3 / ----------- + ----------------------- + ----------------------------------------------|
\ 3 3 9 \ 3 9 3 / 3 / \ 3 3 9 \ 3 9 3 / 3 / | 3 \/ 540 180 _______________________________________|
| / ___________________ |
| / 11680885699 I*\/ 12086728234237311 |
| 9*3 / ----------- + ----------------------- |
\ \/ 540 180 /
$$\left(- \frac{418}{3} - \frac{418 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} + \frac{418 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + i \left(- \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9}\right)\right) \left(\frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418}{3} - \frac{418 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + i \left(\frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3}\right)\right) \left(- \frac{418}{3} + \frac{698896}{9 \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}} + \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}\right)$$
=
/ / / ___________________\\ / / ___________________\\\
| | |3*\/ 12086728234237311 || | |3*\/ 12086728234237311 |||
/ _________________________________________ / ____________________________________________\\ | |atan|-----------------------|| |2*atan|-----------------------|||
| 3 ____ 3 / ___________________ | 3 / ___________________ || | | \ 11680885699 /| | \ 11680885699 /||
87362*\6988960*\/ 20 + \/ 11680885699 + 3*I*\/ 12086728234237311 *\-4180 + \/ 584044284950 + 150*I*\/ 12086728234237311 //*|-3 + 4*cos|-----------------------------| + 8*cos|-------------------------------||
\ \ 3 / \ 3 //
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_________________________________________
3 / ___________________
135*\/ 11680885699 + 3*I*\/ 12086728234237311
$$\frac{87362 \left(6988960 \sqrt[3]{20} + \left(-4180 + \sqrt[3]{584044284950 + 150 \sqrt{12086728234237311} i}\right) \sqrt[3]{11680885699 + 3 \sqrt{12086728234237311} i}\right) \left(-3 + 4 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)} + 8 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}\right)}{135 \sqrt[3]{11680885699 + 3 \sqrt{12086728234237311} i}}$$
87362*(6988960*20^(1/3) + (11680885699 + 3*i*sqrt(12086728234237311))^(1/3)*(-4180 + (584044284950 + 150*i*sqrt(12086728234237311))^(1/3)))*(-3 + 4*cos(atan(3*sqrt(12086728234237311)/11680885699)/3) + 8*cos(2*atan(3*sqrt(12086728234237311)/11680885699)/3))/(135*(11680885699 + 3*i*sqrt(12086728234237311))^(1/3))
Respuesta numérica
[src]
x1 = 417.975327777291
x2 = -422.529196850741 + 1.73472347597681e-18*i
x3 = -413.44613092655
x3 = -413.44613092655