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La ecuación:
Ecuación 3^x=4
Ecuación 6*x^2+x-7=0
Ecuación 15-16x+4x^2=0
Ecuación x^3+4*x^2-4*x-16=0
Expresar {x} en función de y en la ecuación:
6*x-19*y=-18
3*x-12*y=-14
17*x-19*y=-12
-4*x+14*y=-2
Expresiones idénticas
x^ tres - catorce *x^ dos + cuarenta y seis *x- veintiséis = cero
x al cubo menos 14 multiplicar por x al cuadrado más 46 multiplicar por x menos 26 es igual a 0
x en el grado tres menos cotangente de angente de orce multiplicar por x en el grado dos más cuarenta y seis multiplicar por x menos veintiséis es igual a cero
x3-14*x2+46*x-26=0
x³-14*x²+46*x-26=0
x en el grado 3-14*x en el grado 2+46*x-26=0
x^3-14x^2+46x-26=0
x3-14x2+46x-26=0
x^3-14*x^2+46*x-26=O
Expresiones semejantes
x^3-14*x^2+46*x+26=0
x^3-14*x^2-46*x-26=0
x^3+14*x^2+46*x-26=0

x^3-14x^2+46x-26=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3       2                
x  - 14*x  + 46*x - 26 = 0

\left(46 x + \left(x^{3} - 14 x^{2}\right)\right) - 26 = 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 = -14

q = \frac{c}{a}

q = 46

v = \frac{d}{a}

v = -26

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} = 14

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 46

x_{1} x_{2} x_{3} = -26

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

          /                   1                    \     /     /                   1                    \                                                                 \                                                                              /                   1                    \     /     /                   1                    \                                                                 \                                                                                                                              
     58*re|----------------------------------------|     |58*im|----------------------------------------|             /    /    _______\\              /    /    _______\\|             /    /    _______\\              /    /    _______\\        58*re|----------------------------------------|     |58*im|----------------------------------------|             /    /    _______\\              /    /    _______\\|             /    /    _______\\              /    /    _______\\                                                             
          |                     ___________________|     |     |                     ___________________|             |    |3*\/ 17367 ||              |    |3*\/ 17367 |||             |    |3*\/ 17367 ||              |    |3*\/ 17367 ||             |                     ___________________|     |     |                     ___________________|             |    |3*\/ 17367 ||              |    |3*\/ 17367 |||             |    |3*\/ 17367 ||              |    |3*\/ 17367 ||                                                             
          |/          ___\     /           _______ |     |     |/          ___\     /           _______ |             |atan|-----------||              |atan|-----------|||             |atan|-----------||              |atan|-----------||             |/          ___\     /           _______ |     |     |/          ___\     /           _______ |             |atan|-----------||              |atan|-----------|||             |atan|-----------||              |atan|-----------||                                                             
          ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     |     ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     ____    |    \    197    /|     _____    |    \    197    /||     ____    |    \    197    /|     _____    |    \    197    /|             ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     |     ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     ____    |    \    197    /|     _____    |    \    197    /||     ____    |    \    197    /|     _____    |    \    197    /|             ___________________                             
          ||- - - -------|*3 /   --- + ----------- |     |     ||- - - -------|*3 /   --- + ----------- |   \/ 58 *sin|-----------------|   \/ 174 *cos|-----------------||   \/ 58 *cos|-----------------|   \/ 174 *sin|-----------------|             ||- - + -------|*3 /   --- + ----------- |     |     ||- - + -------|*3 /   --- + ----------- |   \/ 58 *sin|-----------------|   \/ 174 *cos|-----------------||   \/ 58 *cos|-----------------|   \/ 174 *sin|-----------------|            /           _______                              
14        \\  2      2   / \/     27        9      /     |     \\  2      2   / \/     27        9      /             \        3        /              \        3        /|             \        3        /              \        3        /   14        \\  2      2   / \/     27        9      /     |     \\  2      2   / \/     27        9      /             \        3        /              \        3        /|             \        3        /              \        3        /   14      /  197   I*\/ 17367                 58            
-- + ----------------------------------------------- + I*|----------------------------------------------- - ----------------------------- - ------------------------------| - ----------------------------- + ------------------------------ + -- + ----------------------------------------------- + I*|----------------------------------------------- - ----------------------------- + ------------------------------| - ----------------------------- - ------------------------------ + -- + 3 /   --- + -----------  + --------------------------
3                           9                            \                       9                                        6                               6               /                 6                               6                  3                           9                            \                       9                                        6                               6               /                 6                               6                  3    \/     27        9                ___________________
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    /           _______ 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   /  197   I*\/ 17367  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              9*3 /   --- + ----------- 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                \/     27        9

\left(\frac{14}{3} + \frac{58}{9 \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}} + \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}\right) + \left(\left(- \frac{\sqrt{58} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{58 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9} + \frac{\sqrt{174} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{14}{3} + i \left(- \frac{\sqrt{174} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} - \frac{\sqrt{58} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{58 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9}\right)\right) + \left(\frac{58 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9} - \frac{\sqrt{58} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} - \frac{\sqrt{174} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{14}{3} + i \left(\frac{58 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9} - \frac{\sqrt{58} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{\sqrt{174} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6}\right)\right)\right)

                                                                  /                   1                    \        /                   1                    \     /     /                   1                    \                                                                 \     /     /                   1                    \                                                                 \                                
                                                             58*re|----------------------------------------|   58*re|----------------------------------------|     |58*im|----------------------------------------|             /    /    _______\\              /    /    _______\\|     |58*im|----------------------------------------|             /    /    _______\\              /    /    _______\\|             /    /    _______\\
                                                                  |                     ___________________|        |                     ___________________|     |     |                     ___________________|             |    |3*\/ 17367 ||              |    |3*\/ 17367 |||     |     |                     ___________________|             |    |3*\/ 17367 ||              |    |3*\/ 17367 |||             |    |3*\/ 17367 ||
                                                                  |/          ___\     /           _______ |        |/          ___\     /           _______ |     |     |/          ___\     /           _______ |             |atan|-----------||              |atan|-----------|||     |     |/          ___\     /           _______ |             |atan|-----------||              |atan|-----------|||             |atan|-----------||
          ___________________                                     ||  1   I*\/ 3 |    /  197   I*\/ 17367  |        ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     |     ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     ____    |    \    197    /|     _____    |    \    197    /||     |     ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     ____    |    \    197    /|     _____    |    \    197    /||     ____    |    \    197    /|
         /           _______                                      ||- - + -------|*3 /   --- + ----------- |        ||- - - -------|*3 /   --- + ----------- |     |     ||- - + -------|*3 /   --- + ----------- |   \/ 58 *sin|-----------------|   \/ 174 *cos|-----------------||     |     ||- - - -------|*3 /   --- + ----------- |   \/ 58 *sin|-----------------|   \/ 174 *cos|-----------------||   \/ 58 *cos|-----------------|
        /  197   I*\/ 17367                 58                    \\  2      2   / \/     27        9      /        \\  2      2   / \/     27        9      /     |     \\  2      2   / \/     27        9      /             \        3        /              \        3        /|     |     \\  2      2   / \/     27        9      /             \        3        /              \        3        /|             \        3        /
14 + 3 /   --- + -----------  + -------------------------- + ----------------------------------------------- + ----------------------------------------------- + I*|----------------------------------------------- - ----------------------------- + ------------------------------| + I*|----------------------------------------------- - ----------------------------- - ------------------------------| - -----------------------------
     \/     27        9                ___________________                          9                                                 9                            \                       9                                        6                               6               /     \                       9                                        6                               6               /                 3              
                                      /           _______                                                                                                                                                                                                                                                                                                                                                                                   
                                     /  197   I*\/ 17367                                                                                                                                                                                                                                                                                                                                                                                    
                                9*3 /   --- + -----------                                                                                                                                                                                                                                                                                                                                                                                   
                                  \/     27        9

- \frac{\sqrt{58} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{3} + \frac{58 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9} + \frac{58 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9} + 14 + \frac{58}{9 \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}} + i \left(- \frac{\sqrt{174} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} - \frac{\sqrt{58} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{58 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9}\right) + i \left(\frac{58 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9} - \frac{\sqrt{58} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{\sqrt{174} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6}\right) + \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}

producto

/          /                   1                    \     /     /                   1                    \                                                                 \                                                                 \ /          /                   1                    \     /     /                   1                    \                                                                 \                                                                 \                                                             
|     58*re|----------------------------------------|     |58*im|----------------------------------------|             /    /    _______\\              /    /    _______\\|             /    /    _______\\              /    /    _______\\| |     58*re|----------------------------------------|     |58*im|----------------------------------------|             /    /    _______\\              /    /    _______\\|             /    /    _______\\              /    /    _______\\|                                                             
|          |                     ___________________|     |     |                     ___________________|             |    |3*\/ 17367 ||              |    |3*\/ 17367 |||             |    |3*\/ 17367 ||              |    |3*\/ 17367 ||| |          |                     ___________________|     |     |                     ___________________|             |    |3*\/ 17367 ||              |    |3*\/ 17367 |||             |    |3*\/ 17367 ||              |    |3*\/ 17367 |||                                                             
|          |/          ___\     /           _______ |     |     |/          ___\     /           _______ |             |atan|-----------||              |atan|-----------|||             |atan|-----------||              |atan|-----------||| |          |/          ___\     /           _______ |     |     |/          ___\     /           _______ |             |atan|-----------||              |atan|-----------|||             |atan|-----------||              |atan|-----------|||                                                             
|          ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     |     ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     ____    |    \    197    /|     _____    |    \    197    /||     ____    |    \    197    /|     _____    |    \    197    /|| |          ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     |     ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     ____    |    \    197    /|     _____    |    \    197    /||     ____    |    \    197    /|     _____    |    \    197    /|| /          ___________________                             \
|          ||- - - -------|*3 /   --- + ----------- |     |     ||- - - -------|*3 /   --- + ----------- |   \/ 58 *sin|-----------------|   \/ 174 *cos|-----------------||   \/ 58 *cos|-----------------|   \/ 174 *sin|-----------------|| |          ||- - + -------|*3 /   --- + ----------- |     |     ||- - + -------|*3 /   --- + ----------- |   \/ 58 *sin|-----------------|   \/ 174 *cos|-----------------||   \/ 58 *cos|-----------------|   \/ 174 *sin|-----------------|| |         /           _______                              |
|14        \\  2      2   / \/     27        9      /     |     \\  2      2   / \/     27        9      /             \        3        /              \        3        /|             \        3        /              \        3        /| |14        \\  2      2   / \/     27        9      /     |     \\  2      2   / \/     27        9      /             \        3        /              \        3        /|             \        3        /              \        3        /| |14      /  197   I*\/ 17367                 58            |
|-- + ----------------------------------------------- + I*|----------------------------------------------- - ----------------------------- - ------------------------------| - ----------------------------- + ------------------------------|*|-- + ----------------------------------------------- + I*|----------------------------------------------- - ----------------------------- + ------------------------------| - ----------------------------- - ------------------------------|*|-- + 3 /   --- + -----------  + --------------------------|
\3                           9                            \                       9                                        6                               6               /                 6                               6               / \3                           9                            \                       9                                        6                               6               /                 6                               6               / |3    \/     27        9                ___________________|
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |                                      /           _______ |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |                                     /  197   I*\/ 17367  |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |                                9*3 /   --- + ----------- |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              \                                  \/     27        9      /

\left(- \frac{\sqrt{58} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{58 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9} + \frac{\sqrt{174} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{14}{3} + i \left(- \frac{\sqrt{174} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} - \frac{\sqrt{58} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{58 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9}\right)\right) \left(\frac{58 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9} - \frac{\sqrt{58} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} - \frac{\sqrt{174} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{14}{3} + i \left(\frac{58 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9} - \frac{\sqrt{58} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{\sqrt{174} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6}\right)\right) \left(\frac{14}{3} + \frac{58}{9 \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}} + \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}\right)

                                                                /             /      /    _______\\                /    /    _______\\\
                                                                |             |      |3*\/ 17367 ||                |    |3*\/ 17367 |||
/        _____________________ /        _____________________\\ |             |2*atan|-----------||                |atan|-----------|||
|     3 /             _______  |     3 /             _______ || |             |      \    197    /|        ____    |    \    197    /||
\58 + \/  197 + 3*I*\/ 17367  *\14 + \/  197 + 3*I*\/ 17367  //*|138 + 116*cos|-------------------| - 28*\/ 58 *cos|-----------------||
                                                                \             \         3         /                \        3        //
---------------------------------------------------------------------------------------------------------------------------------------
                                                            _____________________                                                      
                                                         3 /             _______                                                       
                                                      27*\/  197 + 3*I*\/ 17367

\frac{\left(58 + \left(14 + \sqrt[3]{197 + 3 \sqrt{17367} i}\right) \sqrt[3]{197 + 3 \sqrt{17367} i}\right) \left(- 28 \sqrt{58} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)} + 116 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)} + 138\right)}{27 \sqrt[3]{197 + 3 \sqrt{17367} i}}

(58 + (197 + 3*i*sqrt(17367))^(1/3)*(14 + (197 + 3*i*sqrt(17367))^(1/3)))*(138 + 116*cos(2*atan(3*sqrt(17367)/197)/3) - 28*sqrt(58)*cos(atan(3*sqrt(17367)/197)/3))/(27*(197 + 3*i*sqrt(17367))^(1/3))

Respuesta rápida [src]

               /                   1                    \     /     /                   1                    \                                                                 \                                                                 
          58*re|----------------------------------------|     |58*im|----------------------------------------|             /    /    _______\\              /    /    _______\\|             /    /    _______\\              /    /    _______\\
               |                     ___________________|     |     |                     ___________________|             |    |3*\/ 17367 ||              |    |3*\/ 17367 |||             |    |3*\/ 17367 ||              |    |3*\/ 17367 ||
               |/          ___\     /           _______ |     |     |/          ___\     /           _______ |             |atan|-----------||              |atan|-----------|||             |atan|-----------||              |atan|-----------||
               ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     |     ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     ____    |    \    197    /|     _____    |    \    197    /||     ____    |    \    197    /|     _____    |    \    197    /|
               ||- - - -------|*3 /   --- + ----------- |     |     ||- - - -------|*3 /   --- + ----------- |   \/ 58 *sin|-----------------|   \/ 174 *cos|-----------------||   \/ 58 *cos|-----------------|   \/ 174 *sin|-----------------|
     14        \\  2      2   / \/     27        9      /     |     \\  2      2   / \/     27        9      /             \        3        /              \        3        /|             \        3        /              \        3        /
x1 = -- + ----------------------------------------------- + I*|----------------------------------------------- - ----------------------------- - ------------------------------| - ----------------------------- + ------------------------------
     3                           9                            \                       9                                        6                               6               /                 6                               6

x_{1} = - \frac{\sqrt{58} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{58 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9} + \frac{\sqrt{174} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{14}{3} + i \left(- \frac{\sqrt{174} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} - \frac{\sqrt{58} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{58 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9}\right)

               /                   1                    \     /     /                   1                    \                                                                 \                                                                 
          58*re|----------------------------------------|     |58*im|----------------------------------------|             /    /    _______\\              /    /    _______\\|             /    /    _______\\              /    /    _______\\
               |                     ___________________|     |     |                     ___________________|             |    |3*\/ 17367 ||              |    |3*\/ 17367 |||             |    |3*\/ 17367 ||              |    |3*\/ 17367 ||
               |/          ___\     /           _______ |     |     |/          ___\     /           _______ |             |atan|-----------||              |atan|-----------|||             |atan|-----------||              |atan|-----------||
               ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     |     ||  1   I*\/ 3 |    /  197   I*\/ 17367  |     ____    |    \    197    /|     _____    |    \    197    /||     ____    |    \    197    /|     _____    |    \    197    /|
               ||- - + -------|*3 /   --- + ----------- |     |     ||- - + -------|*3 /   --- + ----------- |   \/ 58 *sin|-----------------|   \/ 174 *cos|-----------------||   \/ 58 *cos|-----------------|   \/ 174 *sin|-----------------|
     14        \\  2      2   / \/     27        9      /     |     \\  2      2   / \/     27        9      /             \        3        /              \        3        /|             \        3        /              \        3        /
x2 = -- + ----------------------------------------------- + I*|----------------------------------------------- - ----------------------------- + ------------------------------| - ----------------------------- - ------------------------------
     3                           9                            \                       9                                        6                               6               /                 6                               6

x_{2} = \frac{58 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9} - \frac{\sqrt{58} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} - \frac{\sqrt{174} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{14}{3} + i \left(\frac{58 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}}\right)}}{9} - \frac{\sqrt{58} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6} + \frac{\sqrt{174} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{17367}}{197} \right)}}{3} \right)}}{6}\right)

               ___________________                             
              /           _______                              
     14      /  197   I*\/ 17367                 58            
x3 = -- + 3 /   --- + -----------  + --------------------------
     3    \/     27        9                ___________________
                                           /           _______ 
                                          /  197   I*\/ 17367  
                                     9*3 /   --- + ----------- 
                                       \/     27        9

x_{3} = \frac{14}{3} + \frac{58}{9 \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}} + \sqrt[3]{\frac{197}{27} + \frac{\sqrt{17367} i}{9}}

x3 = 14/3 + 58/(9*(197/27 + sqrt(17367)*i/9)^(1/3)) + (197/27 + sqrt(17367)*i/9)^(1/3)

Respuesta numérica [src]

x1 = 0.711429966702324

x2 = 3.88740084810372

x3 = 9.40116918519396

x3 = 9.40116918519396

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x^3-14*x^2+46*x-26=0 la ecuación

Solución numérica:

Solución

x^3-14x^2+46x-26=0 la ecuación