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La ecuación:
Ecuación x^2-6x+9=0
Ecuación (x-11)^4=(x+3)^4
Ecuación √(x^2-1)^3=2*x
Ecuación -x/12+x=55/12
Expresar {x} en función de y en la ecuación:
18*x-11*y=2
12*x-14*y=20
-3*x-20*y=-13
-16*x+14*y=-9
Expresiones idénticas
uno *x^ cinco - dos *x- uno = cero
1 multiplicar por x en el grado 5 menos 2 multiplicar por x menos 1 es igual a 0
uno multiplicar por x en el grado cinco menos dos multiplicar por x menos uno es igual a cero
1*x5-2*x-1=0
1*x⁵-2*x-1=0
1x^5-2x-1=0
1x5-2x-1=0
1*x^5-2*x-1=O
Expresiones semejantes
1*x^5+2*x-1=0
1*x^5-2*x+1=0

1x^5-2x-1=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 5              
x  - 2*x - 1 = 0

$$\left(x^{5} - 2 x\right) - 1 = 0$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

x1 = -1

$$x_{1} = -1$$

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                                                                                I*           /    |- - - 2*3 /   --- + --------  - ---------------------------------------------------------------------- + -----------------------| 
                   __________________________________________________________               /     |  6     \/    432     144                   __________________________________________________________          ________________| 
                  /               ________________                                         /      |                                           /               ________________                                    /         ______ | 
                 /               /         ______                                         /       |                                          /               /         ______                                    /   65   \/ 1689  | 
                /     5         /   65   \/ 1689                7                        /        |                                         /     5         /   65   \/ 1689                7               9*3 /   --- + -------- | 
               /    - -- + 2*3 /   --- + --------  - -----------------------            /         |                                4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144    | 
              /       12     \/    432     144              ________________           /          |                                       /       12     \/    432     144              ________________                           | 
             /                                             /         ______           /           |                                      /                                             /         ______                            | 
            /                                             /   65   \/ 1689           /            |                                     /                                             /   65   \/ 1689                             | 
           /                                         9*3 /   --- + --------         /             |                                    /                                         9*3 /   --- + --------                            | 
     1   \/                                            \/    432     144          \/              |                                  \/                                            \/    432     144                               | 
x2 = - - -------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------
     4                                    2                                                                                                               2

$$x_{2} = - \frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4} - \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}} - 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}\right|}}{2}$$

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                   __________________________________________________________               /     |  6     \/    432     144                   __________________________________________________________          ________________| 
                  /               ________________                                         /      |                                           /               ________________                                    /         ______ | 
                 /               /         ______                                         /       |                                          /               /         ______                                    /   65   \/ 1689  | 
                /     5         /   65   \/ 1689                7                        /        |                                         /     5         /   65   \/ 1689                7               9*3 /   --- + -------- | 
               /    - -- + 2*3 /   --- + --------  - -----------------------            /         |                                4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144    | 
              /       12     \/    432     144              ________________           /          |                                       /       12     \/    432     144              ________________                           | 
             /                                             /         ______           /           |                                      /                                             /         ______                            | 
            /                                             /   65   \/ 1689           /            |                                     /                                             /   65   \/ 1689                             | 
           /                                         9*3 /   --- + --------         /             |                                    /                                         9*3 /   --- + --------                            | 
     1   \/                                            \/    432     144          \/              |                                  \/                                            \/    432     144                               | 
x3 = - - -------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------
     4                                    2                                                                                                               2

$$x_{3} = - \frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4} + \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}} - 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}\right|}}{2}$$

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                                                                                            /     5        /   65   \/ 1689                                       5                                                 7            
                                                                                           /    - - - 2*3 /   --- + --------  + ---------------------------------------------------------------------- + ----------------------- 
                   __________________________________________________________             /       6     \/    432     144                   __________________________________________________________          ________________ 
                  /               ________________                                       /                                                 /               ________________                                    /         ______  
                 /               /         ______                                       /                                                 /               /         ______                                    /   65   \/ 1689   
                /     5         /   65   \/ 1689                7                      /                                                 /     5         /   65   \/ 1689                7               9*3 /   --- + --------  
               /    - -- + 2*3 /   --- + --------  - -----------------------          /                                         4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144     
              /       12     \/    432     144              ________________         /                                                 /       12     \/    432     144              ________________                            
             /                                             /         ______         /                                                 /                                             /         ______                             
            /                                             /   65   \/ 1689         /                                                 /                                             /   65   \/ 1689                              
           /                                         9*3 /   --- + --------       /                                                 /                                         9*3 /   --- + --------                             
     1   \/                                            \/    432     144        \/                                                \/                                            \/    432     144                                
x4 = - + -------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------
     4                                    2                                                                                                             2

$$x_{4} = \frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4} + \frac{\sqrt{- 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} + \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}}}{2}$$

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                                                                                            /     5        /   65   \/ 1689                                       5                                                 7            
                                                                                           /    - - - 2*3 /   --- + --------  + ---------------------------------------------------------------------- + ----------------------- 
                   __________________________________________________________             /       6     \/    432     144                   __________________________________________________________          ________________ 
                  /               ________________                                       /                                                 /               ________________                                    /         ______  
                 /               /         ______                                       /                                                 /               /         ______                                    /   65   \/ 1689   
                /     5         /   65   \/ 1689                7                      /                                                 /     5         /   65   \/ 1689                7               9*3 /   --- + --------  
               /    - -- + 2*3 /   --- + --------  - -----------------------          /                                         4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144     
              /       12     \/    432     144              ________________         /                                                 /       12     \/    432     144              ________________                            
             /                                             /         ______         /                                                 /                                             /         ______                             
            /                                             /   65   \/ 1689         /                                                 /                                             /   65   \/ 1689                              
           /                                         9*3 /   --- + --------       /                                                 /                                         9*3 /   --- + --------                             
     1   \/                                            \/    432     144        \/                                                \/                                            \/    432     144                                
x5 = - + -------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------
     4                                    2                                                                                                             2

$$x_{5} = - \frac{\sqrt{- 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} + \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}}}{2} + \frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4}$$

x5 = -sqrt(-2*(65/432 + sqrt(1689)/144)^(1/3) - 5/6 + 7/(9*(65/432 + sqrt(1689)/144)^(1/3)) + 5/(4*sqrt(-7/(9*(65/432 + sqrt(1689)/144)^(1/3)) - 5/12 + 2*(65/432 + sqrt(1689)/144)^(1/3))))/2 + sqrt(-7/(9*(65/432 + sqrt(1689)/144)^(1/3)) - 5/12 + 2*(65/432 + sqrt(1689)/144)^(1/3))/2 + 1/4

Suma y producto de raíces [src]

suma

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                                                                                              /   |  5        /   65   \/ 1689                                       5                                                 7           |                                                                                             /   |  5        /   65   \/ 1689                                       5                                                 7           |                                                                                           /     5        /   65   \/ 1689                                       5                                                 7                                                                                                      /     5        /   65   \/ 1689                                       5                                                 7            
                                                                                I*           /    |- - - 2*3 /   --- + --------  - ---------------------------------------------------------------------- + -----------------------|                                                                               I*           /    |- - - 2*3 /   --- + --------  - ---------------------------------------------------------------------- + -----------------------|                                                                                          /    - - - 2*3 /   --- + --------  + ---------------------------------------------------------------------- + -----------------------                                                                                          /    - - - 2*3 /   --- + --------  + ---------------------------------------------------------------------- + ----------------------- 
                   __________________________________________________________               /     |  6     \/    432     144                   __________________________________________________________          ________________|                  __________________________________________________________               /     |  6     \/    432     144                   __________________________________________________________          ________________|                  __________________________________________________________             /       6     \/    432     144                   __________________________________________________________          ________________                  __________________________________________________________             /       6     \/    432     144                   __________________________________________________________          ________________ 
                  /               ________________                                         /      |                                           /               ________________                                    /         ______ |                 /               ________________                                         /      |                                           /               ________________                                    /         ______ |                 /               ________________                                       /                                                 /               ________________                                    /         ______                  /               ________________                                       /                                                 /               ________________                                    /         ______  
                 /               /         ______                                         /       |                                          /               /         ______                                    /   65   \/ 1689  |                /               /         ______                                         /       |                                          /               /         ______                                    /   65   \/ 1689  |                /               /         ______                                       /                                                 /               /         ______                                    /   65   \/ 1689                  /               /         ______                                       /                                                 /               /         ______                                    /   65   \/ 1689   
                /     5         /   65   \/ 1689                7                        /        |                                         /     5         /   65   \/ 1689                7               9*3 /   --- + -------- |               /     5         /   65   \/ 1689                7                        /        |                                         /     5         /   65   \/ 1689                7               9*3 /   --- + -------- |               /     5         /   65   \/ 1689                7                      /                                                 /     5         /   65   \/ 1689                7               9*3 /   --- + --------                /     5         /   65   \/ 1689                7                      /                                                 /     5         /   65   \/ 1689                7               9*3 /   --- + --------  
               /    - -- + 2*3 /   --- + --------  - -----------------------            /         |                                4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144    |              /    - -- + 2*3 /   --- + --------  - -----------------------            /         |                                4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144    |              /    - -- + 2*3 /   --- + --------  - -----------------------          /                                         4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144                  /    - -- + 2*3 /   --- + --------  - -----------------------          /                                         4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144     
              /       12     \/    432     144              ________________           /          |                                       /       12     \/    432     144              ________________                           |             /       12     \/    432     144              ________________           /          |                                       /       12     \/    432     144              ________________                           |             /       12     \/    432     144              ________________         /                                                 /       12     \/    432     144              ________________                                        /       12     \/    432     144              ________________         /                                                 /       12     \/    432     144              ________________                            
             /                                             /         ______           /           |                                      /                                             /         ______                            |            /                                             /         ______           /           |                                      /                                             /         ______                            |            /                                             /         ______         /                                                 /                                             /         ______                                        /                                             /         ______         /                                                 /                                             /         ______                             
            /                                             /   65   \/ 1689           /            |                                     /                                             /   65   \/ 1689                             |           /                                             /   65   \/ 1689           /            |                                     /                                             /   65   \/ 1689                             |           /                                             /   65   \/ 1689         /                                                 /                                             /   65   \/ 1689                                        /                                             /   65   \/ 1689         /                                                 /                                             /   65   \/ 1689                              
           /                                         9*3 /   --- + --------         /             |                                    /                                         9*3 /   --- + --------                            |          /                                         9*3 /   --- + --------         /             |                                    /                                         9*3 /   --- + --------                            |          /                                         9*3 /   --- + --------       /                                                 /                                         9*3 /   --- + --------                                      /                                         9*3 /   --- + --------       /                                                 /                                         9*3 /   --- + --------                             
     1   \/                                            \/    432     144          \/              |                                  \/                                            \/    432     144                               |    1   \/                                            \/    432     144          \/              |                                  \/                                            \/    432     144                               |    1   \/                                            \/    432     144        \/                                                \/                                            \/    432     144                                   1   \/                                            \/    432     144        \/                                                \/                                            \/    432     144                                
-1 + - - -------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------- + - - -------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------- + - + -------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------- + - + -------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------
     4                                    2                                                                                                               2                                                                             4                                    2                                                                                                               2                                                                             4                                    2                                                                                                             2                                                                           4                                    2                                                                                                             2

$$\left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} + \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}}}{2} + \frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4}\right) + \left(\left(\frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4} + \frac{\sqrt{- 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} + \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}}}{2}\right) + \left(\left(-1 + \left(- \frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4} - \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}} - 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}\right|}}{2}\right)\right) + \left(- \frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4} + \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}} - 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}\right|}}{2}\right)\right)\right)$$

$$0$$

producto

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 |                                                                           I*           /    |- - - 2*3 /   --- + --------  - ---------------------------------------------------------------------- + -----------------------| | |                                                                           I*           /    |- - - 2*3 /   --- + --------  - ---------------------------------------------------------------------- + -----------------------| | |                                                                                      /    - - - 2*3 /   --- + --------  + ---------------------------------------------------------------------- + ----------------------- | |                                                                                      /    - - - 2*3 /   --- + --------  + ---------------------------------------------------------------------- + ----------------------- |
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 |           /     5         /   65   \/ 1689                7                        /        |                                         /     5         /   65   \/ 1689                7               9*3 /   --- + -------- | | |           /     5         /   65   \/ 1689                7                        /        |                                         /     5         /   65   \/ 1689                7               9*3 /   --- + -------- | | |           /     5         /   65   \/ 1689                7                      /                                                 /     5         /   65   \/ 1689                7               9*3 /   --- + --------  | |           /     5         /   65   \/ 1689                7                      /                                                 /     5         /   65   \/ 1689                7               9*3 /   --- + --------  |
 |          /    - -- + 2*3 /   --- + --------  - -----------------------            /         |                                4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144    | | |          /    - -- + 2*3 /   --- + --------  - -----------------------            /         |                                4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144    | | |          /    - -- + 2*3 /   --- + --------  - -----------------------          /                                         4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144     | |          /    - -- + 2*3 /   --- + --------  - -----------------------          /                                         4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144     |
 |         /       12     \/    432     144              ________________           /          |                                       /       12     \/    432     144              ________________                           | | |         /       12     \/    432     144              ________________           /          |                                       /       12     \/    432     144              ________________                           | | |         /       12     \/    432     144              ________________         /                                                 /       12     \/    432     144              ________________                            | |         /       12     \/    432     144              ________________         /                                                 /       12     \/    432     144              ________________                            |
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 |      /                                         9*3 /   --- + --------         /             |                                    /                                         9*3 /   --- + --------                            | | |      /                                         9*3 /   --- + --------         /             |                                    /                                         9*3 /   --- + --------                            | | |      /                                         9*3 /   --- + --------       /                                                 /                                         9*3 /   --- + --------                             | |      /                                         9*3 /   --- + --------       /                                                 /                                         9*3 /   --- + --------                             |
 |1   \/                                            \/    432     144          \/              |                                  \/                                            \/    432     144                               | | |1   \/                                            \/    432     144          \/              |                                  \/                                            \/    432     144                               | | |1   \/                                            \/    432     144        \/                                                \/                                            \/    432     144                                | |1   \/                                            \/    432     144        \/                                                \/                                            \/    432     144                                |
-|- - -------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------|*|- - -------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------|*|- + -------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------|*|- + -------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------|
 \4                                    2                                                                                                               2                                                                          / \4                                    2                                                                                                               2                                                                          / \4                                    2                                                                                                             2                                                                        / \4                                    2                                                                                                             2                                                                        /

$$- (- \frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4} - \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}} - 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}\right|}}{2}) \left(- \frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4} + \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}} - 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}\right|}}{2}\right) \left(\frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4} + \frac{\sqrt{- 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} + \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}}}{2}\right) \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} + \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}}}{2} + \frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4}\right)$$

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|                                                                                             / |             ________________                                                                                                   | | |                                                                                         /              ________________                                                                                                    | |                                                                                         /              ________________                                                                                                    | |                                                                                           / |             ________________                                                                                                   | |
|                                                                                            /  |            /         ______                                                                                                    | | |                                                                                        /              /         ______                                                                                                     | |                                                                                        /              /         ______                                                                                                     | |                                                                                          /  |            /         ______                                                                                                    | |
|                                                                                           /   |  5        /   65   \/ 1689                                       5                                                 7           | | |                                                                                       /     5        /   65   \/ 1689                                       5                                                 7            | |                                                                                       /     5        /   65   \/ 1689                                       5                                                 7            | |                                                                                         /   |  5        /   65   \/ 1689                                       5                                                 7           | |
|                                                                             I*           /    |- - - 2*3 /   --- + --------  - ---------------------------------------------------------------------- + -----------------------| | |                                                                                      /    - - - 2*3 /   --- + --------  + ---------------------------------------------------------------------- + ----------------------- | |                                                                                      /    - - - 2*3 /   --- + --------  + ---------------------------------------------------------------------- + ----------------------- | |                                                                           I*           /    |- - - 2*3 /   --- + --------  - ---------------------------------------------------------------------- + -----------------------| |
|                __________________________________________________________               /     |  6     \/    432     144                   __________________________________________________________          ________________| | |              __________________________________________________________             /       6     \/    432     144                   __________________________________________________________          ________________ | |              __________________________________________________________             /       6     \/    432     144                   __________________________________________________________          ________________ | |              __________________________________________________________               /     |  6     \/    432     144                   __________________________________________________________          ________________| |
|               /               ________________                                         /      |                                           /               ________________                                    /         ______ | | |             /               ________________                                       /                                                 /               ________________                                    /         ______  | |             /               ________________                                       /                                                 /               ________________                                    /         ______  | |             /               ________________                                         /      |                                           /               ________________                                    /         ______ | |
|              /               /         ______                                         /       |                                          /               /         ______                                    /   65   \/ 1689  | | |            /               /         ______                                       /                                                 /               /         ______                                    /   65   \/ 1689   | |            /               /         ______                                       /                                                 /               /         ______                                    /   65   \/ 1689   | |            /               /         ______                                         /       |                                          /               /         ______                                    /   65   \/ 1689  | |
|             /     5         /   65   \/ 1689                7                        /        |                                         /     5         /   65   \/ 1689                7               9*3 /   --- + -------- | | |           /     5         /   65   \/ 1689                7                      /                                                 /     5         /   65   \/ 1689                7               9*3 /   --- + --------  | |           /     5         /   65   \/ 1689                7                      /                                                 /     5         /   65   \/ 1689                7               9*3 /   --- + --------  | |           /     5         /   65   \/ 1689                7                        /        |                                         /     5         /   65   \/ 1689                7               9*3 /   --- + -------- | |
|            /    - -- + 2*3 /   --- + --------  - -----------------------            /         |                                4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144    | | |          /    - -- + 2*3 /   --- + --------  - -----------------------          /                                         4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144     | |          /    - -- + 2*3 /   --- + --------  - -----------------------          /                                         4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144     | |          /    - -- + 2*3 /   --- + --------  - -----------------------            /         |                                4*      /    - -- + 2*3 /   --- + --------  - -----------------------      \/    432     144    | |
|           /       12     \/    432     144              ________________           /          |                                       /       12     \/    432     144              ________________                           | | |         /       12     \/    432     144              ________________         /                                                 /       12     \/    432     144              ________________                            | |         /       12     \/    432     144              ________________         /                                                 /       12     \/    432     144              ________________                            | |         /       12     \/    432     144              ________________           /          |                                       /       12     \/    432     144              ________________                           | |
|          /                                             /         ______           /           |                                      /                                             /         ______                            | | |        /                                             /         ______         /                                                 /                                             /         ______                             | |        /                                             /         ______         /                                                 /                                             /         ______                             | |        /                                             /         ______           /           |                                      /                                             /         ______                            | |
|         /                                             /   65   \/ 1689           /            |                                     /                                             /   65   \/ 1689                             | | |       /                                             /   65   \/ 1689         /                                                 /                                             /   65   \/ 1689                              | |       /                                             /   65   \/ 1689         /                                                 /                                             /   65   \/ 1689                              | |       /                                             /   65   \/ 1689           /            |                                     /                                             /   65   \/ 1689                             | |
|        /                                         9*3 /   --- + --------         /             |                                    /                                         9*3 /   --- + --------                            | | |      /                                         9*3 /   --- + --------       /                                                 /                                         9*3 /   --- + --------                             | |      /                                         9*3 /   --- + --------       /                                                 /                                         9*3 /   --- + --------                             | |      /                                         9*3 /   --- + --------         /             |                                    /                                         9*3 /   --- + --------                            | |
|  1   \/                                            \/    432     144          \/              |                                  \/                                            \/    432     144                               | | |1   \/                                            \/    432     144        \/                                                \/                                            \/    432     144                                | |1   \/                                            \/    432     144        \/                                                \/                                            \/    432     144                                | |1   \/                                            \/    432     144          \/              |                                  \/                                            \/    432     144                               | |
|- - + -------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------|*|- + -------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------|*|- + -------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------|*|- - -------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------|
\  4                                    2                                                                                                               2                                                                          / \4                                    2                                                                                                             2                                                                        / \4                                    2                                                                                                             2                                                                        / \4                                    2                                                                                                               2                                                                          /

$$\left(- \frac{1}{4} + \frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}} - 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}\right|}}{2}\right) \left(- \frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4} + \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}} - 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}\right|}}{2}\right) \left(\frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4} + \frac{\sqrt{- 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} + \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}}}{2}\right) \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}} - \frac{5}{6} + \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} + \frac{5}{4 \sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}}}{2} + \frac{\sqrt{- \frac{7}{9 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}} - \frac{5}{12} + 2 \sqrt[3]{\frac{65}{432} + \frac{\sqrt{1689}}{144}}}}{2} + \frac{1}{4}\right)$$

(-1/4 + sqrt(-5/12 + 2*(65/432 + sqrt(1689)/144)^(1/3) - 7/(9*(65/432 + sqrt(1689)/144)^(1/3)))/2 + i*sqrt(Abs(-5/6 - 2*(65/432 + sqrt(1689)/144)^(1/3) - 5/(4*sqrt(-5/12 + 2*(65/432 + sqrt(1689)/144)^(1/3) - 7/(9*(65/432 + sqrt(1689)/144)^(1/3)))) + 7/(9*(65/432 + sqrt(1689)/144)^(1/3))))/2)*(1/4 + sqrt(-5/12 + 2*(65/432 + sqrt(1689)/144)^(1/3) - 7/(9*(65/432 + sqrt(1689)/144)^(1/3)))/2 + sqrt(-5/6 - 2*(65/432 + sqrt(1689)/144)^(1/3) + 5/(4*sqrt(-5/12 + 2*(65/432 + sqrt(1689)/144)^(1/3) - 7/(9*(65/432 + sqrt(1689)/144)^(1/3)))) + 7/(9*(65/432 + sqrt(1689)/144)^(1/3)))/2)*(1/4 + sqrt(-5/12 + 2*(65/432 + sqrt(1689)/144)^(1/3) - 7/(9*(65/432 + sqrt(1689)/144)^(1/3)))/2 - sqrt(-5/6 - 2*(65/432 + sqrt(1689)/144)^(1/3) + 5/(4*sqrt(-5/12 + 2*(65/432 + sqrt(1689)/144)^(1/3) - 7/(9*(65/432 + sqrt(1689)/144)^(1/3)))) + 7/(9*(65/432 + sqrt(1689)/144)^(1/3)))/2)*(1/4 - sqrt(-5/12 + 2*(65/432 + sqrt(1689)/144)^(1/3) - 7/(9*(65/432 + sqrt(1689)/144)^(1/3)))/2 + i*sqrt(Abs(-5/6 - 2*(65/432 + sqrt(1689)/144)^(1/3) - 5/(4*sqrt(-5/12 + 2*(65/432 + sqrt(1689)/144)^(1/3) - 7/(9*(65/432 + sqrt(1689)/144)^(1/3)))) + 7/(9*(65/432 + sqrt(1689)/144)^(1/3))))/2)

Respuesta numérica [src]

x1 = 1.29064880134671

x2 = -1.0

x3 = 0.114070631164587 - 1.21674600397435*i

x4 = -0.518790063675884

x5 = 0.114070631164587 + 1.21674600397435*i

x5 = 0.114070631164587 + 1.21674600397435*i

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