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La ecuación:
Ecuación x-4/3+x+1/4=3
Ecuación 11x+12y+13z=14a+15b+16c
Ecuación 2x²+13-13x=x+1
Ecuación 2x^2+13x=0
Expresar {x} en función de y en la ecuación:
-13*x-12*y=-11
-13*x+13*y=-20
-10*x-18*y=14
4*x+7*y=1
Expresiones idénticas
uno *x^ tres + cuatrocientos dieciocho *x^ dos - cuatrocientos dieciocho ^2x-(cuatrocientos dieciocho ^ tres - diecisiete mil doscientos cuarenta y dos . tres)= cero
1 multiplicar por x al cubo más 418 multiplicar por x al cuadrado menos 418 al cuadrado x menos (418 al cubo menos 17242.3) es igual a 0
uno multiplicar por x en el grado tres más cuatrocientos dieciocho multiplicar por x en el grado dos menos cuatrocientos dieciocho al cuadrado x menos (cuatrocientos dieciocho en el grado tres menos diecisiete mil doscientos cuarenta y dos . tres) es igual a cero
1*x3+418*x2-4182x-(4183-17242.3)=0
1*x3+418*x2-4182x-4183-17242.3=0
1*x³+418*x²-418²x-(418³-17242.3)=0
1*x en el grado 3+418*x en el grado 2-418 en el grado 2x-(418 en el grado 3-17242.3)=0
1x^3+418x^2-418^2x-(418^3-17242.3)=0
1x3+418x2-4182x-(4183-17242.3)=0
1x3+418x2-4182x-4183-17242.3=0
1x^3+418x^2-418^2x-418^3-17242.3=0
1*x^3+418*x^2-418^2x-(418^3-17242.3)=O
Expresiones semejantes
1*x^3-418*x^2-418^2x-(418^3-17242.3)=0
1*x^3+418*x^2+418^2x-(418^3-17242.3)=0
1*x^3+418*x^2-418^2x-(418^3+17242.3)=0
1*x^3+418*x^2-418^2x+(418^3-17242.3)=0

1x^3+418x^2-418^2x-(418^3-17242.3)=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3        2                          172423    
x  + 418*x  - 174724*x + -73034632 + ------ = 0
                                       10

\left(- 174724 x + \left(x^{3} + 418 x^{2}\right)\right) + \left(-73034632 + \frac{172423}{10}\right) = 0

Simplificar

Teorema de Cardano-Vieta

es ecuación cúbica reducida

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

donde

p = \frac{b}{a}

p = 418

q = \frac{c}{a}

q = -174724

v = \frac{d}{a}

v = -73034632 + \frac{172423}{10}

Fórmulas de Cardano-Vieta

x_{1} + x_{2} + x_{3} = - p

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

x_{1} x_{2} x_{3} = v

x_{1} + x_{2} + x_{3} = -418

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -174724

x_{1} x_{2} x_{3} = -73034632 + \frac{172423}{10}

Respuesta rápida [src]

                                                               /                             1                              \     /                                                    /                             1                              \                                               \                                               
                    /    /    ___________________\\   698896*re|------------------------------------------------------------|     |         /    /    ___________________\\   698896*im|------------------------------------------------------------|                /    /    ___________________\\|                /    /    ___________________\\
                    |    |3*\/ 12086728234237311 ||            |                     _______________________________________|     |         |    |3*\/ 12086728234237311 ||            |                     _______________________________________|                |    |3*\/ 12086728234237311 |||                |    |3*\/ 12086728234237311 ||
                    |atan|-----------------------||            |/          ___\     /                   ___________________ |     |         |atan|-----------------------||            |/          ___\     /                   ___________________ |                |atan|-----------------------|||                |atan|-----------------------||
                    |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |     |         |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |         ___    |    \      11680885699      /||         ___    |    \      11680885699      /|
             418*cos|-----------------------------|            ||- - - -------|*3 /   ----------- + ----------------------- |     |  418*sin|-----------------------------|            ||- - - -------|*3 /   ----------- + ----------------------- |   418*\/ 3 *cos|-----------------------------||   418*\/ 3 *sin|-----------------------------|
       418          \              3              /            \\  2      2   / \/        540                 180           /     |         \              3              /            \\  2      2   / \/        540                 180           /                \              3              /|                \              3              /
x1 = - --- - -------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- - --------------------------------------------| + --------------------------------------------
        3                      3                                                         9                                        \                    3                                                         9                                                           3                      /                        3

x_{1} = - \frac{418}{3} - \frac{418 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} + \frac{418 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + i \left(- \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9}\right)

                                                               /                             1                              \     /                                                    /                             1                              \                                               \                                               
                    /    /    ___________________\\   698896*re|------------------------------------------------------------|     |         /    /    ___________________\\   698896*im|------------------------------------------------------------|                /    /    ___________________\\|                /    /    ___________________\\
                    |    |3*\/ 12086728234237311 ||            |                     _______________________________________|     |         |    |3*\/ 12086728234237311 ||            |                     _______________________________________|                |    |3*\/ 12086728234237311 |||                |    |3*\/ 12086728234237311 ||
                    |atan|-----------------------||            |/          ___\     /                   ___________________ |     |         |atan|-----------------------||            |/          ___\     /                   ___________________ |                |atan|-----------------------|||                |atan|-----------------------||
                    |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |     |         |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |         ___    |    \      11680885699      /||         ___    |    \      11680885699      /|
             418*cos|-----------------------------|            ||- - + -------|*3 /   ----------- + ----------------------- |     |  418*sin|-----------------------------|            ||- - + -------|*3 /   ----------- + ----------------------- |   418*\/ 3 *cos|-----------------------------||   418*\/ 3 *sin|-----------------------------|
       418          \              3              /            \\  2      2   / \/        540                 180           /     |         \              3              /            \\  2      2   / \/        540                 180           /                \              3              /|                \              3              /
x2 = - --- - -------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- + --------------------------------------------| - --------------------------------------------
        3                      3                                                         9                                        \                    3                                                         9                                                           3                      /                        3

x_{2} = \frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418}{3} - \frac{418 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + i \left(\frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3}\right)

                  _______________________________________                                                 
                 /                   ___________________                                                  
       418      /  11680885699   I*\/ 12086728234237311                         698896                    
x3 = - --- + 3 /   ----------- + -----------------------  + ----------------------------------------------
        3    \/        540                 180                     _______________________________________
                                                                  /                   ___________________ 
                                                                 /  11680885699   I*\/ 12086728234237311  
                                                            9*3 /   ----------- + ----------------------- 
                                                              \/        540                 180

x_{3} = - \frac{418}{3} + \frac{698896}{9 \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}} + \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}

x3 = -418/3 + 698896/(9*(11680885699/540 + sqrt(12086728234237311)*i/180)^(1/3)) + (11680885699/540 + sqrt(12086728234237311)*i/180)^(1/3)

Suma y producto de raíces [src]

suma

                                                          /                             1                              \     /                                                    /                             1                              \                                               \                                                                                                            /                             1                              \     /                                                    /                             1                              \                                               \                                                                                                                                                       
               /    /    ___________________\\   698896*re|------------------------------------------------------------|     |         /    /    ___________________\\   698896*im|------------------------------------------------------------|                /    /    ___________________\\|                /    /    ___________________\\                  /    /    ___________________\\   698896*re|------------------------------------------------------------|     |         /    /    ___________________\\   698896*im|------------------------------------------------------------|                /    /    ___________________\\|                /    /    ___________________\\                                                                                                        
               |    |3*\/ 12086728234237311 ||            |                     _______________________________________|     |         |    |3*\/ 12086728234237311 ||            |                     _______________________________________|                |    |3*\/ 12086728234237311 |||                |    |3*\/ 12086728234237311 ||                  |    |3*\/ 12086728234237311 ||            |                     _______________________________________|     |         |    |3*\/ 12086728234237311 ||            |                     _______________________________________|                |    |3*\/ 12086728234237311 |||                |    |3*\/ 12086728234237311 ||                                                                                                        
               |atan|-----------------------||            |/          ___\     /                   ___________________ |     |         |atan|-----------------------||            |/          ___\     /                   ___________________ |                |atan|-----------------------|||                |atan|-----------------------||                  |atan|-----------------------||            |/          ___\     /                   ___________________ |     |         |atan|-----------------------||            |/          ___\     /                   ___________________ |                |atan|-----------------------|||                |atan|-----------------------||                                                                                                        
               |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |     |         |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |         ___    |    \      11680885699      /||         ___    |    \      11680885699      /|                  |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |     |         |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |         ___    |    \      11680885699      /||         ___    |    \      11680885699      /|                _______________________________________                                                 
        418*cos|-----------------------------|            ||- - - -------|*3 /   ----------- + ----------------------- |     |  418*sin|-----------------------------|            ||- - - -------|*3 /   ----------- + ----------------------- |   418*\/ 3 *cos|-----------------------------||   418*\/ 3 *sin|-----------------------------|           418*cos|-----------------------------|            ||- - + -------|*3 /   ----------- + ----------------------- |     |  418*sin|-----------------------------|            ||- - + -------|*3 /   ----------- + ----------------------- |   418*\/ 3 *cos|-----------------------------||   418*\/ 3 *sin|-----------------------------|               /                   ___________________                                                  
  418          \              3              /            \\  2      2   / \/        540                 180           /     |         \              3              /            \\  2      2   / \/        540                 180           /                \              3              /|                \              3              /     418          \              3              /            \\  2      2   / \/        540                 180           /     |         \              3              /            \\  2      2   / \/        540                 180           /                \              3              /|                \              3              /     418      /  11680885699   I*\/ 12086728234237311                         698896                    
- --- - -------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- - --------------------------------------------| + -------------------------------------------- + - --- - -------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- + --------------------------------------------| - -------------------------------------------- + - --- + 3 /   ----------- + -----------------------  + ----------------------------------------------
   3                      3                                                         9                                        \                    3                                                         9                                                           3                      /                        3                            3                      3                                                         9                                        \                    3                                                         9                                                           3                      /                        3                            3    \/        540                 180                     _______________________________________
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /                   ___________________ 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /  11680885699   I*\/ 12086728234237311  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           9*3 /   ----------- + ----------------------- 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \/        540                 180

\left(- \frac{418}{3} + \frac{698896}{9 \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}} + \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}\right) + \left(\left(\frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418}{3} - \frac{418 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + i \left(\frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3}\right)\right) + \left(- \frac{418}{3} - \frac{418 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} + \frac{418 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + i \left(- \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9}\right)\right)\right)

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                                                             /    /    ___________________\\                                                    698896*re|------------------------------------------------------------|   698896*re|------------------------------------------------------------|     |         /    /    ___________________\\   698896*im|------------------------------------------------------------|                /    /    ___________________\\|     |         /    /    ___________________\\   698896*im|------------------------------------------------------------|                /    /    ___________________\\|
                                                             |    |3*\/ 12086728234237311 ||                                                             |                     _______________________________________|            |                     _______________________________________|     |         |    |3*\/ 12086728234237311 ||            |                     _______________________________________|                |    |3*\/ 12086728234237311 |||     |         |    |3*\/ 12086728234237311 ||            |                     _______________________________________|                |    |3*\/ 12086728234237311 |||
                                                             |atan|-----------------------||                                                             |/          ___\     /                   ___________________ |            |/          ___\     /                   ___________________ |     |         |atan|-----------------------||            |/          ___\     /                   ___________________ |                |atan|-----------------------|||     |         |atan|-----------------------||            |/          ___\     /                   ___________________ |                |atan|-----------------------|||
            _______________________________________          |    \      11680885699      /|                                                             ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |     |         |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |         ___    |    \      11680885699      /||     |         |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |         ___    |    \      11680885699      /||
           /                   ___________________    836*cos|-----------------------------|                                                             ||- - + -------|*3 /   ----------- + ----------------------- |            ||- - - -------|*3 /   ----------- + ----------------------- |     |  418*sin|-----------------------------|            ||- - + -------|*3 /   ----------- + ----------------------- |   418*\/ 3 *cos|-----------------------------||     |  418*sin|-----------------------------|            ||- - - -------|*3 /   ----------- + ----------------------- |   418*\/ 3 *cos|-----------------------------||
          /  11680885699   I*\/ 12086728234237311            \              3              /                       698896                                \\  2      2   / \/        540                 180           /            \\  2      2   / \/        540                 180           /     |         \              3              /            \\  2      2   / \/        540                 180           /                \              3              /|     |         \              3              /            \\  2      2   / \/        540                 180           /                \              3              /|
-418 + 3 /   ----------- + -----------------------  - -------------------------------------- + ---------------------------------------------- + ----------------------------------------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- + --------------------------------------------| + I*|- -------------------------------------- + ----------------------------------------------------------------------- - --------------------------------------------|
       \/        540                 180                                3                             _______________________________________                                      9                                                                         9                                        \                    3                                                         9                                                           3                      /     \                    3                                                         9                                                           3                      /
                                                                                                     /                   ___________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
                                                                                                    /  11680885699   I*\/ 12086728234237311                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      
                                                                                               9*3 /   ----------- + -----------------------                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
                                                                                                 \/        540                 180

-418 - \frac{836 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} + \frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} + \frac{698896}{9 \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}} + i \left(\frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3}\right) + i \left(- \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9}\right) + \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}

producto

/                                                          /                             1                              \     /                                                    /                             1                              \                                               \                                               \ /                                                          /                             1                              \     /                                                    /                             1                              \                                               \                                               \                                                                                                        
|               /    /    ___________________\\   698896*re|------------------------------------------------------------|     |         /    /    ___________________\\   698896*im|------------------------------------------------------------|                /    /    ___________________\\|                /    /    ___________________\\| |               /    /    ___________________\\   698896*re|------------------------------------------------------------|     |         /    /    ___________________\\   698896*im|------------------------------------------------------------|                /    /    ___________________\\|                /    /    ___________________\\|                                                                                                        
|               |    |3*\/ 12086728234237311 ||            |                     _______________________________________|     |         |    |3*\/ 12086728234237311 ||            |                     _______________________________________|                |    |3*\/ 12086728234237311 |||                |    |3*\/ 12086728234237311 ||| |               |    |3*\/ 12086728234237311 ||            |                     _______________________________________|     |         |    |3*\/ 12086728234237311 ||            |                     _______________________________________|                |    |3*\/ 12086728234237311 |||                |    |3*\/ 12086728234237311 |||                                                                                                        
|               |atan|-----------------------||            |/          ___\     /                   ___________________ |     |         |atan|-----------------------||            |/          ___\     /                   ___________________ |                |atan|-----------------------|||                |atan|-----------------------||| |               |atan|-----------------------||            |/          ___\     /                   ___________________ |     |         |atan|-----------------------||            |/          ___\     /                   ___________________ |                |atan|-----------------------|||                |atan|-----------------------|||                                                                                                        
|               |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |     |         |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |         ___    |    \      11680885699      /||         ___    |    \      11680885699      /|| |               |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |     |         |    \      11680885699      /|            ||  1   I*\/ 3 |    /  11680885699   I*\/ 12086728234237311  |         ___    |    \      11680885699      /||         ___    |    \      11680885699      /|| /             _______________________________________                                                 \
|        418*cos|-----------------------------|            ||- - - -------|*3 /   ----------- + ----------------------- |     |  418*sin|-----------------------------|            ||- - - -------|*3 /   ----------- + ----------------------- |   418*\/ 3 *cos|-----------------------------||   418*\/ 3 *sin|-----------------------------|| |        418*cos|-----------------------------|            ||- - + -------|*3 /   ----------- + ----------------------- |     |  418*sin|-----------------------------|            ||- - + -------|*3 /   ----------- + ----------------------- |   418*\/ 3 *cos|-----------------------------||   418*\/ 3 *sin|-----------------------------|| |            /                   ___________________                                                  |
|  418          \              3              /            \\  2      2   / \/        540                 180           /     |         \              3              /            \\  2      2   / \/        540                 180           /                \              3              /|                \              3              /| |  418          \              3              /            \\  2      2   / \/        540                 180           /     |         \              3              /            \\  2      2   / \/        540                 180           /                \              3              /|                \              3              /| |  418      /  11680885699   I*\/ 12086728234237311                         698896                    |
|- --- - -------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- - --------------------------------------------| + --------------------------------------------|*|- --- - -------------------------------------- + ----------------------------------------------------------------------- + I*|- -------------------------------------- + ----------------------------------------------------------------------- + --------------------------------------------| - --------------------------------------------|*|- --- + 3 /   ----------- + -----------------------  + ----------------------------------------------|
\   3                      3                                                         9                                        \                    3                                                         9                                                           3                      /                        3                      / \   3                      3                                                         9                                        \                    3                                                         9                                                           3                      /                        3                      / |   3    \/        540                 180                     _______________________________________|
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |                                                            /  11680885699   I*\/ 12086728234237311  |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |                                                       9*3 /   ----------- + ----------------------- |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    \                                                         \/        540                 180           /

\left(- \frac{418}{3} - \frac{418 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} + \frac{418 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + i \left(- \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9}\right)\right) \left(\frac{698896 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418}{3} - \frac{418 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} - \frac{418 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + i \left(\frac{698896 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}}\right)}}{9} - \frac{418 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3} + \frac{418 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}}{3}\right)\right) \left(- \frac{418}{3} + \frac{698896}{9 \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}} + \sqrt[3]{\frac{11680885699}{540} + \frac{\sqrt{12086728234237311} i}{180}}\right)

                                                                                                                                /          /    /    ___________________\\        /      /    ___________________\\\
                                                                                                                                |          |    |3*\/ 12086728234237311 ||        |      |3*\/ 12086728234237311 |||
      /                    _________________________________________ /           ____________________________________________\\ |          |atan|-----------------------||        |2*atan|-----------------------|||
      |        3 ____   3 /                     ___________________  |        3 /                        ___________________ || |          |    \      11680885699      /|        |      \      11680885699      /||
87362*\6988960*\/ 20  + \/  11680885699 + 3*I*\/ 12086728234237311  *\-4180 + \/  584044284950 + 150*I*\/ 12086728234237311  //*|-3 + 4*cos|-----------------------------| + 8*cos|-------------------------------||
                                                                                                                                \          \              3              /        \               3               //
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                         _________________________________________                                                                                  
                                                                                      3 /                     ___________________                                                                                   
                                                                                  135*\/  11680885699 + 3*I*\/ 12086728234237311

\frac{87362 \left(6988960 \sqrt[3]{20} + \left(-4180 + \sqrt[3]{584044284950 + 150 \sqrt{12086728234237311} i}\right) \sqrt[3]{11680885699 + 3 \sqrt{12086728234237311} i}\right) \left(-3 + 4 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)} + 8 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{3 \sqrt{12086728234237311}}{11680885699} \right)}}{3} \right)}\right)}{135 \sqrt[3]{11680885699 + 3 \sqrt{12086728234237311} i}}

87362*(6988960*20^(1/3) + (11680885699 + 3*i*sqrt(12086728234237311))^(1/3)*(-4180 + (584044284950 + 150*i*sqrt(12086728234237311))^(1/3)))*(-3 + 4*cos(atan(3*sqrt(12086728234237311)/11680885699)/3) + 8*cos(2*atan(3*sqrt(12086728234237311)/11680885699)/3))/(135*(11680885699 + 3*i*sqrt(12086728234237311))^(1/3))

Respuesta numérica [src]

x1 = 417.975327777291

x2 = -422.529196850741 + 1.73472347597681e-18*i

x3 = -413.44613092655

x3 = -413.44613092655

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1*x^3+418*x^2-418^2x-(418^3-17242.3)=0 la ecuación

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