Sr Examen

Lang:

Otras calculadoras

¿Cómo usar?
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
Gráfico de la función y =:
2*x^3+9*x^2-24*x-56
Expresiones idénticas
dos *x^ tres + nueve *x^ dos - veinticuatro *x- cincuenta y seis = cero
2 multiplicar por x al cubo más 9 multiplicar por x al cuadrado menos 24 multiplicar por x menos 56 es igual a 0
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
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

2x^3+9x^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

Simplificar

Teorema de Cardano-Vieta

reescribamos la ecuación

\left(- 24 x + \left(2 x^{3} + 9 x^{2}\right)\right) - 56 = 0

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

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

2*x^3+9*x^2-24*x-56=0 la ecuación

Solución numérica:

Solución

2x^3+9x^2-24*x-56=0 la ecuación