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3*(x-1)*(x^2-3*x+1)^2+(x^2-3*x+1)^2=4*(x-1)^2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
                        2                 2             
          / 2          \    / 2          \             2
3*(x - 1)*\x  - 3*x + 1/  + \x  - 3*x + 1/  = 4*(x - 1) 
$$3 \left(x - 1\right) \left(\left(x^{2} - 3 x\right) + 1\right)^{2} + \left(\left(x^{2} - 3 x\right) + 1\right)^{2} = 4 \left(x - 1\right)^{2}$$
Gráfica
Respuesta rápida [src]
x1 = 2
$$x_{1} = 2$$
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                                                                                           /   10        /  683    \/ 831                 23                                               152                                   
                                                                                          /    -- - 2*3 /   ---- + -------  + ------------------------- + ---------------------------------------------------------------------- 
                   _________________________________________________________             /     3      \/    5832     243               ________________                _________________________________________________________ 
                  /            ________________                                         /                                             /          _____                /            ________________                              
                 /            /          _____                                         /                                             /  683    \/ 831                /            /          _____                               
                /   5        /  683    \/ 831                 23                      /                                       162*3 /   ---- + -------              /   5        /  683    \/ 831                 23             
               /    - + 2*3 /   ---- + -------  - -------------------------          /                                            \/    5832     243      27*      /    - + 2*3 /   ---- + -------  - -------------------------  
              /     3     \/    5832     243               ________________         /                                                                             /     3     \/    5832     243               ________________  
             /                                            /          _____         /                                                                             /                                            /          _____   
            /                                            /  683    \/ 831         /                                                                             /                                            /  683    \/ 831    
           /                                      162*3 /   ---- + -------       /                                                                             /                                      162*3 /   ---- + -------   
     7   \/                                           \/    5832     243       \/                                                                            \/                                           \/    5832     243     
x2 = - + ------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------
     6                                    2                                                                                                            2                                                                         
$$x_{2} = \frac{\sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}{2} + \frac{7}{6} + \frac{\sqrt{- 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + \frac{10}{3} + \frac{152}{27 \sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}}}{2}$$
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                                                                                           /   10        /  683    \/ 831                 23                                               152                                   
                                                                                          /    -- - 2*3 /   ---- + -------  + ------------------------- + ---------------------------------------------------------------------- 
                   _________________________________________________________             /     3      \/    5832     243               ________________                _________________________________________________________ 
                  /            ________________                                         /                                             /          _____                /            ________________                              
                 /            /          _____                                         /                                             /  683    \/ 831                /            /          _____                               
                /   5        /  683    \/ 831                 23                      /                                       162*3 /   ---- + -------              /   5        /  683    \/ 831                 23             
               /    - + 2*3 /   ---- + -------  - -------------------------          /                                            \/    5832     243      27*      /    - + 2*3 /   ---- + -------  - -------------------------  
              /     3     \/    5832     243               ________________         /                                                                             /     3     \/    5832     243               ________________  
             /                                            /          _____         /                                                                             /                                            /          _____   
            /                                            /  683    \/ 831         /                                                                             /                                            /  683    \/ 831    
           /                                      162*3 /   ---- + -------       /                                                                             /                                      162*3 /   ---- + -------   
     7   \/                                           \/    5832     243       \/                                                                            \/                                           \/    5832     243     
x3 = - + ------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------
     6                                    2                                                                                                            2                                                                         
$$x_{3} = - \frac{\sqrt{- 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + \frac{10}{3} + \frac{152}{27 \sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}}}{2} + \frac{\sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}{2} + \frac{7}{6}$$
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                                                                                             /     10        /  683    \/ 831                 23                                               152                                   
                                                                               I*           /    - -- + 2*3 /   ---- + -------  - ------------------------- + ---------------------------------------------------------------------- 
                   _________________________________________________________               /       3      \/    5832     243               ________________                _________________________________________________________ 
                  /            ________________                                           /                                               /          _____                /            ________________                              
                 /            /          _____                                           /                                               /  683    \/ 831                /            /          _____                               
                /   5        /  683    \/ 831                 23                        /                                         162*3 /   ---- + -------              /   5        /  683    \/ 831                 23             
               /    - + 2*3 /   ---- + -------  - -------------------------            /                                              \/    5832     243      27*      /    - + 2*3 /   ---- + -------  - -------------------------  
              /     3     \/    5832     243               ________________           /                                                                               /     3     \/    5832     243               ________________  
             /                                            /          _____           /                                                                               /                                            /          _____   
            /                                            /  683    \/ 831           /                                                                               /                                            /  683    \/ 831    
           /                                      162*3 /   ---- + -------         /                                                                               /                                      162*3 /   ---- + -------   
     7   \/                                           \/    5832     243         \/                                                                              \/                                           \/    5832     243     
x4 = - - ------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------
     6                                    2                                                                                                              2                                                                           
$$x_{4} = - \frac{\sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}{2} + \frac{7}{6} - \frac{i \sqrt{- \frac{10}{3} - \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{152}{27 \sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}}}{2}$$
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                                                                                               /               ________________                                                                                                      
                                                                                              /               /          _____                                                                                                       
                                                                                             /     10        /  683    \/ 831                 23                                               152                                   
                                                                               I*           /    - -- + 2*3 /   ---- + -------  - ------------------------- + ---------------------------------------------------------------------- 
                   _________________________________________________________               /       3      \/    5832     243               ________________                _________________________________________________________ 
                  /            ________________                                           /                                               /          _____                /            ________________                              
                 /            /          _____                                           /                                               /  683    \/ 831                /            /          _____                               
                /   5        /  683    \/ 831                 23                        /                                         162*3 /   ---- + -------              /   5        /  683    \/ 831                 23             
               /    - + 2*3 /   ---- + -------  - -------------------------            /                                              \/    5832     243      27*      /    - + 2*3 /   ---- + -------  - -------------------------  
              /     3     \/    5832     243               ________________           /                                                                               /     3     \/    5832     243               ________________  
             /                                            /          _____           /                                                                               /                                            /          _____   
            /                                            /  683    \/ 831           /                                                                               /                                            /  683    \/ 831    
           /                                      162*3 /   ---- + -------         /                                                                               /                                      162*3 /   ---- + -------   
     7   \/                                           \/    5832     243         \/                                                                              \/                                           \/    5832     243     
x5 = - - ------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------
     6                                    2                                                                                                              2                                                                           
$$x_{5} = - \frac{\sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}{2} + \frac{7}{6} + \frac{i \sqrt{- \frac{10}{3} - \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{152}{27 \sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}}}{2}$$
x5 = -sqrt(-23/(162*(683/5832 + sqrt(831)/243)^(1/3)) + 2*(683/5832 + sqrt(831)/243)^(1/3) + 5/3)/2 + 7/6 + i*sqrt(-10/3 - 23/(162*(683/5832 + sqrt(831)/243)^(1/3)) + 2*(683/5832 + sqrt(831)/243)^(1/3) + 152/(27*sqrt(-23/(162*(683/5832 + sqrt(831)/243)^(1/3)) + 2*(683/5832 + sqrt(831)/243)^(1/3) + 5/3)))/2
Suma y producto de raíces [src]
suma
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                                                                                            /             ________________                                                                                                                                                                                                 /             ________________                                                                                                                                                                                                   /               ________________                                                                                                                                                                                                   /               ________________                                                                                                      
                                                                                           /             /          _____                                                                                                                                                                                                 /             /          _____                                                                                                                                                                                                   /               /          _____                                                                                                                                                                                                   /               /          _____                                                                                                       
                                                                                          /   10        /  683    \/ 831                 23                                               152                                                                                                                            /   10        /  683    \/ 831                 23                                               152                                                                                                                              /     10        /  683    \/ 831                 23                                               152                                                                                                                              /     10        /  683    \/ 831                 23                                               152                                   
                                                                                         /    -- - 2*3 /   ---- + -------  + ------------------------- + ----------------------------------------------------------------------                                                                                         /    -- - 2*3 /   ---- + -------  + ------------------------- + ----------------------------------------------------------------------                                                                              I*           /    - -- + 2*3 /   ---- + -------  - ------------------------- + ----------------------------------------------------------------------                                                                              I*           /    - -- + 2*3 /   ---- + -------  - ------------------------- + ---------------------------------------------------------------------- 
                  _________________________________________________________             /     3      \/    5832     243               ________________                _________________________________________________________                  _________________________________________________________             /     3      \/    5832     243               ________________                _________________________________________________________                  _________________________________________________________               /       3      \/    5832     243               ________________                _________________________________________________________                  _________________________________________________________               /       3      \/    5832     243               ________________                _________________________________________________________ 
                 /            ________________                                         /                                             /          _____                /            ________________                                              /            ________________                                         /                                             /          _____                /            ________________                                              /            ________________                                           /                                               /          _____                /            ________________                                              /            ________________                                           /                                               /          _____                /            ________________                              
                /            /          _____                                         /                                             /  683    \/ 831                /            /          _____                                              /            /          _____                                         /                                             /  683    \/ 831                /            /          _____                                              /            /          _____                                           /                                               /  683    \/ 831                /            /          _____                                              /            /          _____                                           /                                               /  683    \/ 831                /            /          _____                               
               /   5        /  683    \/ 831                 23                      /                                       162*3 /   ---- + -------              /   5        /  683    \/ 831                 23                           /   5        /  683    \/ 831                 23                      /                                       162*3 /   ---- + -------              /   5        /  683    \/ 831                 23                           /   5        /  683    \/ 831                 23                        /                                         162*3 /   ---- + -------              /   5        /  683    \/ 831                 23                           /   5        /  683    \/ 831                 23                        /                                         162*3 /   ---- + -------              /   5        /  683    \/ 831                 23             
              /    - + 2*3 /   ---- + -------  - -------------------------          /                                            \/    5832     243      27*      /    - + 2*3 /   ---- + -------  - -------------------------               /    - + 2*3 /   ---- + -------  - -------------------------          /                                            \/    5832     243      27*      /    - + 2*3 /   ---- + -------  - -------------------------               /    - + 2*3 /   ---- + -------  - -------------------------            /                                              \/    5832     243      27*      /    - + 2*3 /   ---- + -------  - -------------------------               /    - + 2*3 /   ---- + -------  - -------------------------            /                                              \/    5832     243      27*      /    - + 2*3 /   ---- + -------  - -------------------------  
             /     3     \/    5832     243               ________________         /                                                                             /     3     \/    5832     243               ________________              /     3     \/    5832     243               ________________         /                                                                             /     3     \/    5832     243               ________________              /     3     \/    5832     243               ________________           /                                                                               /     3     \/    5832     243               ________________              /     3     \/    5832     243               ________________           /                                                                               /     3     \/    5832     243               ________________  
            /                                            /          _____         /                                                                             /                                            /          _____              /                                            /          _____         /                                                                             /                                            /          _____              /                                            /          _____           /                                                                               /                                            /          _____              /                                            /          _____           /                                                                               /                                            /          _____   
           /                                            /  683    \/ 831         /                                                                             /                                            /  683    \/ 831              /                                            /  683    \/ 831         /                                                                             /                                            /  683    \/ 831              /                                            /  683    \/ 831           /                                                                               /                                            /  683    \/ 831              /                                            /  683    \/ 831           /                                                                               /                                            /  683    \/ 831    
          /                                      162*3 /   ---- + -------       /                                                                             /                                      162*3 /   ---- + -------            /                                      162*3 /   ---- + -------       /                                                                             /                                      162*3 /   ---- + -------            /                                      162*3 /   ---- + -------         /                                                                               /                                      162*3 /   ---- + -------            /                                      162*3 /   ---- + -------         /                                                                               /                                      162*3 /   ---- + -------   
    7   \/                                           \/    5832     243       \/                                                                            \/                                           \/    5832     243        7   \/                                           \/    5832     243       \/                                                                            \/                                           \/    5832     243        7   \/                                           \/    5832     243         \/                                                                              \/                                           \/    5832     243        7   \/                                           \/    5832     243         \/                                                                              \/                                           \/    5832     243     
2 + - + ------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------- + - + ------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------- + - - ------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------ + - - ------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------
    6                                    2                                                                                                            2                                                                            6                                    2                                                                                                            2                                                                            6                                    2                                                                                                              2                                                                              6                                    2                                                                                                              2                                                                           
$$\left(\left(\left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + \frac{10}{3} + \frac{152}{27 \sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}}}{2} + \frac{\sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}{2} + \frac{7}{6}\right) + \left(2 + \left(\frac{\sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}{2} + \frac{7}{6} + \frac{\sqrt{- 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + \frac{10}{3} + \frac{152}{27 \sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}}}{2}\right)\right)\right) + \left(- \frac{\sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}{2} + \frac{7}{6} - \frac{i \sqrt{- \frac{10}{3} - \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{152}{27 \sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}}}{2}\right)\right) + \left(- \frac{\sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}{2} + \frac{7}{6} + \frac{i \sqrt{- \frac{10}{3} - \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{152}{27 \sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}}}{2}\right)$$
=
20/3
$$\frac{20}{3}$$
producto
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  |                                                                                      /   10        /  683    \/ 831                 23                                               152                                   | |                                                                                      /   10        /  683    \/ 831                 23                                               152                                   | |                                                                                        /     10        /  683    \/ 831                 23                                               152                                   | |                                                                                        /     10        /  683    \/ 831                 23                                               152                                   |
  |                                                                                     /    -- - 2*3 /   ---- + -------  + ------------------------- + ---------------------------------------------------------------------- | |                                                                                     /    -- - 2*3 /   ---- + -------  + ------------------------- + ---------------------------------------------------------------------- | |                                                                          I*           /    - -- + 2*3 /   ---- + -------  - ------------------------- + ---------------------------------------------------------------------- | |                                                                          I*           /    - -- + 2*3 /   ---- + -------  - ------------------------- + ---------------------------------------------------------------------- |
  |              _________________________________________________________             /     3      \/    5832     243               ________________                _________________________________________________________ | |              _________________________________________________________             /     3      \/    5832     243               ________________                _________________________________________________________ | |              _________________________________________________________               /       3      \/    5832     243               ________________                _________________________________________________________ | |              _________________________________________________________               /       3      \/    5832     243               ________________                _________________________________________________________ |
  |             /            ________________                                         /                                             /          _____                /            ________________                              | |             /            ________________                                         /                                             /          _____                /            ________________                              | |             /            ________________                                           /                                               /          _____                /            ________________                              | |             /            ________________                                           /                                               /          _____                /            ________________                              |
  |            /            /          _____                                         /                                             /  683    \/ 831                /            /          _____                               | |            /            /          _____                                         /                                             /  683    \/ 831                /            /          _____                               | |            /            /          _____                                           /                                               /  683    \/ 831                /            /          _____                               | |            /            /          _____                                           /                                               /  683    \/ 831                /            /          _____                               |
  |           /   5        /  683    \/ 831                 23                      /                                       162*3 /   ---- + -------              /   5        /  683    \/ 831                 23             | |           /   5        /  683    \/ 831                 23                      /                                       162*3 /   ---- + -------              /   5        /  683    \/ 831                 23             | |           /   5        /  683    \/ 831                 23                        /                                         162*3 /   ---- + -------              /   5        /  683    \/ 831                 23             | |           /   5        /  683    \/ 831                 23                        /                                         162*3 /   ---- + -------              /   5        /  683    \/ 831                 23             |
  |          /    - + 2*3 /   ---- + -------  - -------------------------          /                                            \/    5832     243      27*      /    - + 2*3 /   ---- + -------  - -------------------------  | |          /    - + 2*3 /   ---- + -------  - -------------------------          /                                            \/    5832     243      27*      /    - + 2*3 /   ---- + -------  - -------------------------  | |          /    - + 2*3 /   ---- + -------  - -------------------------            /                                              \/    5832     243      27*      /    - + 2*3 /   ---- + -------  - -------------------------  | |          /    - + 2*3 /   ---- + -------  - -------------------------            /                                              \/    5832     243      27*      /    - + 2*3 /   ---- + -------  - -------------------------  |
  |         /     3     \/    5832     243               ________________         /                                                                             /     3     \/    5832     243               ________________  | |         /     3     \/    5832     243               ________________         /                                                                             /     3     \/    5832     243               ________________  | |         /     3     \/    5832     243               ________________           /                                                                               /     3     \/    5832     243               ________________  | |         /     3     \/    5832     243               ________________           /                                                                               /     3     \/    5832     243               ________________  |
  |        /                                            /          _____         /                                                                             /                                            /          _____   | |        /                                            /          _____         /                                                                             /                                            /          _____   | |        /                                            /          _____           /                                                                               /                                            /          _____   | |        /                                            /          _____           /                                                                               /                                            /          _____   |
  |       /                                            /  683    \/ 831         /                                                                             /                                            /  683    \/ 831    | |       /                                            /  683    \/ 831         /                                                                             /                                            /  683    \/ 831    | |       /                                            /  683    \/ 831           /                                                                               /                                            /  683    \/ 831    | |       /                                            /  683    \/ 831           /                                                                               /                                            /  683    \/ 831    |
  |      /                                      162*3 /   ---- + -------       /                                                                             /                                      162*3 /   ---- + -------   | |      /                                      162*3 /   ---- + -------       /                                                                             /                                      162*3 /   ---- + -------   | |      /                                      162*3 /   ---- + -------         /                                                                               /                                      162*3 /   ---- + -------   | |      /                                      162*3 /   ---- + -------         /                                                                               /                                      162*3 /   ---- + -------   |
  |7   \/                                           \/    5832     243       \/                                                                            \/                                           \/    5832     243     | |7   \/                                           \/    5832     243       \/                                                                            \/                                           \/    5832     243     | |7   \/                                           \/    5832     243         \/                                                                              \/                                           \/    5832     243     | |7   \/                                           \/    5832     243         \/                                                                              \/                                           \/    5832     243     |
2*|- + ------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------|*|- + ------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------|*|- - ------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------|*|- - ------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------|
  \6                                    2                                                                                                            2                                                                         / \6                                    2                                                                                                            2                                                                         / \6                                    2                                                                                                              2                                                                           / \6                                    2                                                                                                              2                                                                           /
$$2 \left(\frac{\sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}{2} + \frac{7}{6} + \frac{\sqrt{- 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + \frac{10}{3} + \frac{152}{27 \sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}}}{2}\right) \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + \frac{10}{3} + \frac{152}{27 \sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}}}{2} + \frac{\sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}{2} + \frac{7}{6}\right) \left(- \frac{\sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}{2} + \frac{7}{6} - \frac{i \sqrt{- \frac{10}{3} - \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{152}{27 \sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}}}{2}\right) \left(- \frac{\sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}{2} + \frac{7}{6} + \frac{i \sqrt{- \frac{10}{3} - \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{152}{27 \sqrt{- \frac{23}{162 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}}} + 2 \sqrt[3]{\frac{683}{5832} + \frac{\sqrt{831}}{243}} + \frac{5}{3}}}}}{2}\right)$$
=
2
$$2$$
2
Respuesta numérica [src]
x1 = 0.349302066204099 - 0.528230179337553*i
x2 = 2.0
x3 = 0.349302066204099 + 0.528230179337553*i
x4 = 3.18522123636154
x5 = 0.782841297896925
x5 = 0.782841297896925