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La ecuación:
Ecuación 2x=1
Ecuación 3^x=6
Ecuación x:(-6)=55
Ecuación 3+11y=203+y
Expresar {x} en función de y en la ecuación:
-17*x+6*y=14
20*x-8*y=13
4*x-1*y=12
-6*x-13*y=15
Expresiones idénticas
x^ tres +(tres i*x^ dos)-(3*(uno -2i)x)+ diez -5i= cero
x al cubo más (3i multiplicar por x al cuadrado ) menos (3 multiplicar por (1 menos 2i)x) más 10 menos 5i es igual a 0
x en el grado tres más (tres i multiplicar por x en el grado dos) menos (3 multiplicar por (uno menos 2i)x) más diez menos 5i es igual a cero
x3+(3i*x2)-(3*(1-2i)x)+10-5i=0
x3+3i*x2-3*1-2ix+10-5i=0
x³+(3i*x²)-(3*(1-2i)x)+10-5i=0
x en el grado 3+(3i*x en el grado 2)-(3*(1-2i)x)+10-5i=0
x^3+(3ix^2)-(3(1-2i)x)+10-5i=0
x3+(3ix2)-(3(1-2i)x)+10-5i=0
x3+3ix2-31-2ix+10-5i=0
x^3+3ix^2-31-2ix+10-5i=0
x^3+(3i*x^2)-(3*(1-2i)x)+10-5i=O
Expresiones semejantes
x^3+(3i*x^2)+(3*(1-2i)x)+10-5i=0
x^3+(3i*x^2)-(3*(1-2i)x)-10-5i=0
x^3+(3i*x^2)-(3*(1-2i)x)+10+5i=0
x^3-(3i*x^2)-(3*(1-2i)x)+10-5i=0
x^3+(3i*x^2)-(3*(1+2i)x)+10-5i=0

x^3+(3ix^2)-(3(1-2i)x)+10-5i=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3        2                               
x  + 3*I*x  - 3*(1 - 2*I)*x + 10 - 5*I = 0

\left(\left(- x 3 \left(1 - 2 i\right) + \left(x^{3} + 3 i x^{2}\right)\right) + 10\right) - 5 i = 0

Simplificar

Teorema de Cardano-Vieta

es ecuación cúbica reducida

p x^{2} + q x + v + x^{3} = 0

donde

p = \frac{b}{a}

p = 3 i

q = \frac{c}{a}

q = -3 + 6 i

v = \frac{d}{a}

v = 10 - 5 i

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} = - 3 i

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -3 + 6 i

x_{1} x_{2} x_{3} = 10 - 5 i

Gráfica

Respuesta rápida [src]

                                                                                                                         /                                                                                                                                                                                                                 /    / /           ___ 4 ____    /atan(2/3)\\ \\                                                                                                     /    / /           ___ 4 ____    /atan(2/3)\\ \\\                                                                                               /    / /           ___ 4 ____    /atan(2/3)\\ \\                                                                                                     /    / /           ___ 4 ____    /atan(2/3)\\ \\
                                                                                                                         |                                                                                                                                                                                                                 |    |-|-54 - 54*\/ 5 *\/ 13 *sin|---------|| ||                                                                                                     |    |-|-54 - 54*\/ 5 *\/ 13 *sin|---------|| |||                                                                                               |    |-|-54 - 54*\/ 5 *\/ 13 *sin|---------|| ||                                                                                                     |    |-|-54 - 54*\/ 5 *\/ 13 *sin|---------|| ||
                                                                                                                         |                                                                                                                                                                                                                 |    | \                         \    2    // ||                                                                                                     |    | \                         \    2    // |||                                                                                               |    | \                         \    2    // ||                                                                                                     |    | \                         \    2    // ||
                                                                                                                         |                                                                                                                                                                                                                 |atan|----------------------------------------||                                                                                                     |atan|----------------------------------------|||                                                                                               |atan|----------------------------------------||                                                                                                     |atan|----------------------------------------||
                                                                                                                         |                                                                                                                          ___________________________________________________________________________________    |    |             ___ 4 ____    /atan(2/3)\  ||              ___________________________________________________________________________________    |    |             ___ 4 ____    /atan(2/3)\  |||        ___________________________________________________________________________________    |    |             ___ 4 ____    /atan(2/3)\  ||              ___________________________________________________________________________________    |    |             ___ 4 ____    /atan(2/3)\  ||
                                                                                                                         |                                                                                                                         /                                       2                                         2     |    |  216 + 54*\/ 5 *\/ 13 *cos|---------|  ||             /                                       2                                         2     |    |  216 + 54*\/ 5 *\/ 13 *cos|---------|  |||       /                                       2                                         2     |    |  216 + 54*\/ 5 *\/ 13 *cos|---------|  ||             /                                       2                                         2     |    |  216 + 54*\/ 5 *\/ 13 *cos|---------|  ||
                                                                                                                         |                                                                                                                        /  /           ___ 4 ____    /atan(2/3)\\    /           ___ 4 ____    /atan(2/3)\\      |    \                           \    2    /  /|     ___    /  /           ___ 4 ____    /atan(2/3)\\    /           ___ 4 ____    /atan(2/3)\\      |    \                           \    2    /  /||      /  /           ___ 4 ____    /atan(2/3)\\    /           ___ 4 ____    /atan(2/3)\\      |    \                           \    2    /  /|     ___    /  /           ___ 4 ____    /atan(2/3)\\    /           ___ 4 ____    /atan(2/3)\\      |    \                           \    2    /  /|
                                                                                                                         |                                                                                                                     6 /   |-54 - 54*\/ 5 *\/ 13 *sin|---------||  + |216 + 54*\/ 5 *\/ 13 *cos|---------||  *sin|----------------------------------------------|   \/ 3 *6 /   |-54 - 54*\/ 5 *\/ 13 *sin|---------||  + |216 + 54*\/ 5 *\/ 13 *cos|---------||  *cos|----------------------------------------------||   6 /   |-54 - 54*\/ 5 *\/ 13 *sin|---------||  + |216 + 54*\/ 5 *\/ 13 *cos|---------||  *cos|----------------------------------------------|   \/ 3 *6 /   |-54 - 54*\/ 5 *\/ 13 *sin|---------||  + |216 + 54*\/ 5 *\/ 13 *cos|---------||  *sin|----------------------------------------------|
           /                                                   1                                                   \     |         /                                                   1                                                   \   \/    \                         \    2    //    \                         \    2    //      \                      3                       /         \/    \                         \    2    //    \                         \    2    //      \                      3                       /|   \/    \                         \    2    //    \                         \    2    //      \                      3                       /         \/    \                         \    2    //    \                         \    2    //      \                      3                       /
x1 = - 6*im|-------------------------------------------------------------------------------------------------------| + I*|-1 + 6*re|-------------------------------------------------------------------------------------------------------| - -------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------
           |                      _________________________________________________________________________________|     |         |                      _________________________________________________________________________________|                                                                        6                                                                                                                                                 6                                                                         |                                                                        6                                                                                                                                                 6                                                                         
           |                     /          ____________________________________________                           |     |         |                     /          ____________________________________________                           |                                                                                                                                                                                                                                                                                                    |                                                                                                                                                                                                                                                                                                    
           |/          ___\     /          /                                2                                      |     |         |/          ___\     /          /                                2                                      |                                                                                                                                                                                                                                                                                                    |                                                                                                                                                                                                                                                                                                    
           ||  1   I*\/ 3 |    /         \/  (270 - 189*I - 27*I*(-3 + 6*I))  - 23328*I    189*I   27*I*(-3 + 6*I) |     |         ||  1   I*\/ 3 |    /         \/  (270 - 189*I - 27*I*(-3 + 6*I))  - 23328*I    189*I   27*I*(-3 + 6*I) |                                                                                                                                                                                                                                                                                                    |                                                                                                                                                                                                                                                                                                    
           ||- - - -------|*3 /    135 + ----------------------------------------------- - ----- - --------------- |     |         ||- - - -------|*3 /    135 + ----------------------------------------------- - ----- - --------------- |                                                                                                                                                                                                                                                                                                    |                                                                                                                                                                                                                                                                                                    
           \\  2      2   / \/                                  2                            2            2        /     \         \\  2      2   / \/                                  2                            2            2        /                                                                                                                                                                                                                                                                                                    /

x_{1} = - 6 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{135 - \frac{189 i}{2} + \frac{\sqrt{\left(270 - 189 i - 27 i \left(-3 + 6 i\right)\right)^{2} - 23328 i}}{2} - \frac{27 i \left(-3 + 6 i\right)}{2}}}\right)} + \frac{\sqrt{3} \sqrt[6]{\left(- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54\right)^{2} + \left(216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan}{\left(- \frac{- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54}{216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}} \right)}}{3} \right)}}{6} + \frac{\sqrt[6]{\left(- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54\right)^{2} + \left(216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan}{\left(- \frac{- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54}{216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}} \right)}}{3} \right)}}{6} + i \left(-1 + 6 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{135 - \frac{189 i}{2} + \frac{\sqrt{\left(270 - 189 i - 27 i \left(-3 + 6 i\right)\right)^{2} - 23328 i}}{2} - \frac{27 i \left(-3 + 6 i\right)}{2}}}\right)} - \frac{\sqrt[6]{\left(- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54\right)^{2} + \left(216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan}{\left(- \frac{- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54}{216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}} \right)}}{3} \right)}}{6} + \frac{\sqrt{3} \sqrt[6]{\left(- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54\right)^{2} + \left(216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan}{\left(- \frac{- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54}{216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}} \right)}}{3} \right)}}{6}\right)

       /                           /    / /           ___ 4 ____    /atan(2/3)\\ \\                                                                                                                 /    / /           ___ 4 ____    /atan(2/3)\\ \\\                         /    / /           ___ 4 ____    /atan(2/3)\\ \\                                                                                                                 /    / /           ___ 4 ____    /atan(2/3)\\ \\
       |                           |    |-|-54 - 54*\/ 5 *\/ 13 *sin|---------|| ||                                                                                                                 |    |-|-54 - 54*\/ 5 *\/ 13 *sin|---------|| |||                         |    |-|-54 - 54*\/ 5 *\/ 13 *sin|---------|| ||                                                                                                                 |    |-|-54 - 54*\/ 5 *\/ 13 *sin|---------|| ||
       |                           |    | \                         \    2    // ||                                                                                                                 |    | \                         \    2    // |||                         |    | \                         \    2    // ||                                                                                                                 |    | \                         \    2    // ||
       |                           |atan|----------------------------------------||                                                                                                                 |atan|----------------------------------------|||                         |atan|----------------------------------------||                                                                                                                 |atan|----------------------------------------||
       |                           |    |             ___ 4 ____    /atan(2/3)\  ||                          ___________________________________________________________________________________    |    |             ___ 4 ____    /atan(2/3)\  |||                         |    |             ___ 4 ____    /atan(2/3)\  ||                          ___________________________________________________________________________________    |    |             ___ 4 ____    /atan(2/3)\  ||
       |                           |    |  216 + 54*\/ 5 *\/ 13 *cos|---------|  ||                         /                                       2                                         2     |    |  216 + 54*\/ 5 *\/ 13 *cos|---------|  |||                         |    |  216 + 54*\/ 5 *\/ 13 *cos|---------|  ||                         /                                       2                                         2     |    |  216 + 54*\/ 5 *\/ 13 *cos|---------|  ||
       |                           |    \                           \    2    /  /|                        /  /           ___ 4 ____    /atan(2/3)\\    /           ___ 4 ____    /atan(2/3)\\      |    \                           \    2    /  /||                         |    \                           \    2    /  /|                        /  /           ___ 4 ____    /atan(2/3)\\    /           ___ 4 ____    /atan(2/3)\\      |    \                           \    2    /  /|
       |                      6*cos|----------------------------------------------|                     6 /   |-54 - 54*\/ 5 *\/ 13 *sin|---------||  + |216 + 54*\/ 5 *\/ 13 *cos|---------||  *sin|----------------------------------------------||                    6*sin|----------------------------------------------|                     6 /   |-54 - 54*\/ 5 *\/ 13 *sin|---------||  + |216 + 54*\/ 5 *\/ 13 *cos|---------||  *cos|----------------------------------------------|
       |                           \                      3                       /                     \/    \                         \    2    //    \                         \    2    //      \                      3                       /|                         \                      3                       /                     \/    \                         \    2    //    \                         \    2    //      \                      3                       /
x2 = I*|-1 + ---------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------
       |          ___________________________________________________________________________________                                                                        3                                                                      |        ___________________________________________________________________________________                                                                        3                                                                      
       |         /                                       2                                         2                                                                                                                                                |       /                                       2                                         2                                                                                                                                                
       |        /  /           ___ 4 ____    /atan(2/3)\\    /           ___ 4 ____    /atan(2/3)\\                                                                                                                                                 |      /  /           ___ 4 ____    /atan(2/3)\\    /           ___ 4 ____    /atan(2/3)\\                                                                                                                                                 
       |     6 /   |-54 - 54*\/ 5 *\/ 13 *sin|---------||  + |216 + 54*\/ 5 *\/ 13 *cos|---------||                                                                                                                                                 |   6 /   |-54 - 54*\/ 5 *\/ 13 *sin|---------||  + |216 + 54*\/ 5 *\/ 13 *cos|---------||                                                                                                                                                 
       \     \/    \                         \    2    //    \                         \    2    //                                                                                                                                                 /   \/    \                         \    2    //    \                         \    2    //

x_{2} = - \frac{\sqrt[6]{\left(- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54\right)^{2} + \left(216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan}{\left(- \frac{- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54}{216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}} \right)}}{3} \right)}}{3} - \frac{6 \sin{\left(\frac{\operatorname{atan}{\left(- \frac{- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54}{216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}} \right)}}{3} \right)}}{\sqrt[6]{\left(- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54\right)^{2} + \left(216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}\right)^{2}}} + i \left(-1 + \frac{\sqrt[6]{\left(- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54\right)^{2} + \left(216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan}{\left(- \frac{- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54}{216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}} \right)}}{3} \right)}}{3} + \frac{6 \cos{\left(\frac{\operatorname{atan}{\left(- \frac{- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54}{216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}} \right)}}{3} \right)}}{\sqrt[6]{\left(- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54\right)^{2} + \left(216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}\right)^{2}}}\right)

                                                                                                                         /                                                                                                                                                                                                                 /    / /           ___ 4 ____    /atan(2/3)\\ \\                                                                                                     /    / /           ___ 4 ____    /atan(2/3)\\ \\\                                                                                               /    / /           ___ 4 ____    /atan(2/3)\\ \\                                                                                                     /    / /           ___ 4 ____    /atan(2/3)\\ \\
                                                                                                                         |                                                                                                                                                                                                                 |    |-|-54 - 54*\/ 5 *\/ 13 *sin|---------|| ||                                                                                                     |    |-|-54 - 54*\/ 5 *\/ 13 *sin|---------|| |||                                                                                               |    |-|-54 - 54*\/ 5 *\/ 13 *sin|---------|| ||                                                                                                     |    |-|-54 - 54*\/ 5 *\/ 13 *sin|---------|| ||
                                                                                                                         |                                                                                                                                                                                                                 |    | \                         \    2    // ||                                                                                                     |    | \                         \    2    // |||                                                                                               |    | \                         \    2    // ||                                                                                                     |    | \                         \    2    // ||
                                                                                                                         |                                                                                                                                                                                                                 |atan|----------------------------------------||                                                                                                     |atan|----------------------------------------|||                                                                                               |atan|----------------------------------------||                                                                                                     |atan|----------------------------------------||
                                                                                                                         |                                                                                                                          ___________________________________________________________________________________    |    |             ___ 4 ____    /atan(2/3)\  ||              ___________________________________________________________________________________    |    |             ___ 4 ____    /atan(2/3)\  |||        ___________________________________________________________________________________    |    |             ___ 4 ____    /atan(2/3)\  ||              ___________________________________________________________________________________    |    |             ___ 4 ____    /atan(2/3)\  ||
                                                                                                                         |                                                                                                                         /                                       2                                         2     |    |  216 + 54*\/ 5 *\/ 13 *cos|---------|  ||             /                                       2                                         2     |    |  216 + 54*\/ 5 *\/ 13 *cos|---------|  |||       /                                       2                                         2     |    |  216 + 54*\/ 5 *\/ 13 *cos|---------|  ||             /                                       2                                         2     |    |  216 + 54*\/ 5 *\/ 13 *cos|---------|  ||
                                                                                                                         |                                                                                                                        /  /           ___ 4 ____    /atan(2/3)\\    /           ___ 4 ____    /atan(2/3)\\      |    \                           \    2    /  /|     ___    /  /           ___ 4 ____    /atan(2/3)\\    /           ___ 4 ____    /atan(2/3)\\      |    \                           \    2    /  /||      /  /           ___ 4 ____    /atan(2/3)\\    /           ___ 4 ____    /atan(2/3)\\      |    \                           \    2    /  /|     ___    /  /           ___ 4 ____    /atan(2/3)\\    /           ___ 4 ____    /atan(2/3)\\      |    \                           \    2    /  /|
                                                                                                                         |                                                                                                                     6 /   |-54 - 54*\/ 5 *\/ 13 *sin|---------||  + |216 + 54*\/ 5 *\/ 13 *cos|---------||  *sin|----------------------------------------------|   \/ 3 *6 /   |-54 - 54*\/ 5 *\/ 13 *sin|---------||  + |216 + 54*\/ 5 *\/ 13 *cos|---------||  *cos|----------------------------------------------||   6 /   |-54 - 54*\/ 5 *\/ 13 *sin|---------||  + |216 + 54*\/ 5 *\/ 13 *cos|---------||  *cos|----------------------------------------------|   \/ 3 *6 /   |-54 - 54*\/ 5 *\/ 13 *sin|---------||  + |216 + 54*\/ 5 *\/ 13 *cos|---------||  *sin|----------------------------------------------|
           /                                                   1                                                   \     |         /                                                   1                                                   \   \/    \                         \    2    //    \                         \    2    //      \                      3                       /         \/    \                         \    2    //    \                         \    2    //      \                      3                       /|   \/    \                         \    2    //    \                         \    2    //      \                      3                       /         \/    \                         \    2    //    \                         \    2    //      \                      3                       /
x3 = - 6*im|-------------------------------------------------------------------------------------------------------| + I*|-1 + 6*re|-------------------------------------------------------------------------------------------------------| - -------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------
           |                      _________________________________________________________________________________|     |         |                      _________________________________________________________________________________|                                                                        6                                                                                                                                                 6                                                                         |                                                                        6                                                                                                                                                 6                                                                         
           |                     /          ____________________________________________                           |     |         |                     /          ____________________________________________                           |                                                                                                                                                                                                                                                                                                    |                                                                                                                                                                                                                                                                                                    
           |/          ___\     /          /                                2                                      |     |         |/          ___\     /          /                                2                                      |                                                                                                                                                                                                                                                                                                    |                                                                                                                                                                                                                                                                                                    
           ||  1   I*\/ 3 |    /         \/  (270 - 189*I - 27*I*(-3 + 6*I))  - 23328*I    189*I   27*I*(-3 + 6*I) |     |         ||  1   I*\/ 3 |    /         \/  (270 - 189*I - 27*I*(-3 + 6*I))  - 23328*I    189*I   27*I*(-3 + 6*I) |                                                                                                                                                                                                                                                                                                    |                                                                                                                                                                                                                                                                                                    
           ||- - + -------|*3 /    135 + ----------------------------------------------- - ----- - --------------- |     |         ||- - + -------|*3 /    135 + ----------------------------------------------- - ----- - --------------- |                                                                                                                                                                                                                                                                                                    |                                                                                                                                                                                                                                                                                                    
           \\  2      2   / \/                                  2                            2            2        /     \         \\  2      2   / \/                                  2                            2            2        /                                                                                                                                                                                                                                                                                                    /

x_{3} = - \frac{\sqrt{3} \sqrt[6]{\left(- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54\right)^{2} + \left(216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan}{\left(- \frac{- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54}{216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}} \right)}}{3} \right)}}{6} - 6 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{135 - \frac{189 i}{2} + \frac{\sqrt{\left(270 - 189 i - 27 i \left(-3 + 6 i\right)\right)^{2} - 23328 i}}{2} - \frac{27 i \left(-3 + 6 i\right)}{2}}}\right)} + \frac{\sqrt[6]{\left(- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54\right)^{2} + \left(216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan}{\left(- \frac{- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54}{216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}} \right)}}{3} \right)}}{6} + i \left(- \frac{\sqrt{3} \sqrt[6]{\left(- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54\right)^{2} + \left(216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan}{\left(- \frac{- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54}{216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}} \right)}}{3} \right)}}{6} - 1 + 6 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{135 - \frac{189 i}{2} + \frac{\sqrt{\left(270 - 189 i - 27 i \left(-3 + 6 i\right)\right)^{2} - 23328 i}}{2} - \frac{27 i \left(-3 + 6 i\right)}{2}}}\right)} - \frac{\sqrt[6]{\left(- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54\right)^{2} + \left(216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan}{\left(- \frac{- 54 \sqrt[4]{13} \sqrt{5} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)} - 54}{216 + 54 \sqrt[4]{13} \sqrt{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{2} \right)}} \right)}}{3} \right)}}{6}\right)

x3 = -sqrt(3)*((-54*13^(1/4)*sqrt(5)*sin(atan(2/3)/2) - 54)^2 + (216 + 54*13^(1/4)*sqrt(5)*cos(atan(2/3)/2))^2)^(1/6)*sin(atan(-(-54*13^(1/4)*sqrt(5)*sin(atan(2/3)/2) - 54)/(216 + 54*13^(1/4)*sqrt(5)*cos(atan(2/3)/2)))/3)/6 - 6*im(1/((-1/2 + sqrt(3)*i/2)*(135 - 189*i/2 + sqrt((270 - 189*i - 27*i*(-3 + 6*i))^2 - 23328*i)/2 - 27*i*(-3 + 6*i)/2)^(1/3))) + ((-54*13^(1/4)*sqrt(5)*sin(atan(2/3)/2) - 54)^2 + (216 + 54*13^(1/4)*sqrt(5)*cos(atan(2/3)/2))^2)^(1/6)*cos(atan(-(-54*13^(1/4)*sqrt(5)*sin(atan(2/3)/2) - 54)/(216 + 54*13^(1/4)*sqrt(5)*cos(atan(2/3)/2)))/3)/6 + i*(-sqrt(3)*((-54*13^(1/4)*sqrt(5)*sin(atan(2/3)/2) - 54)^2 + (216 + 54*13^(1/4)*sqrt(5)*cos(atan(2/3)/2))^2)^(1/6)*cos(atan(-(-54*13^(1/4)*sqrt(5)*sin(atan(2/3)/2) - 54)/(216 + 54*13^(1/4)*sqrt(5)*cos(atan(2/3)/2)))/3)/6 - 1 + 6*re(1/((-1/2 + sqrt(3)*i/2)*(135 - 189*i/2 + sqrt((270 - 189*i - 27*i*(-3 + 6*i))^2 - 23328*i)/2 - 27*i*(-3 + 6*i)/2)^(1/3))) - ((-54*13^(1/4)*sqrt(5)*sin(atan(2/3)/2) - 54)^2 + (216 + 54*13^(1/4)*sqrt(5)*cos(atan(2/3)/2))^2)^(1/6)*sin(atan(-(-54*13^(1/4)*sqrt(5)*sin(atan(2/3)/2) - 54)/(216 + 54*13^(1/4)*sqrt(5)*cos(atan(2/3)/2)))/3)/6)

Respuesta numérica [src]

x1 = 1.78428740225808 - 3.64955865171258*i

x2 = 0.833361970306632 + 0.641023196786008*i

x3 = -2.61764937256471 + 0.00853545492657097*i

x3 = -2.61764937256471 + 0.00853545492657097*i

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