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x^4-2*x^3-4*x^2-2*x+16=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
 4      3      2               
x  - 2*x  - 4*x  - 2*x + 16 = 0
$$\left(- 2 x + \left(- 4 x^{2} + \left(x^{4} - 2 x^{3}\right)\right)\right) + 16 = 0$$
Gráfica
Respuesta rápida [src]
                                                                                               _________________________________________________________________________________________________________________________________
                                                                                              /             _________________                                                                                                   
                                                                                             /             /          ______                                                                                                    
                                                                                            /   22        /  1615   \/ 8961                                      14                                               98            
                                                                                           /    -- - 2*3 /   ---- + --------  + -------------------------------------------------------------------- - ------------------------ 
                   __________________________________________________________             /     3      \/    108       12                 __________________________________________________________          _________________ 
                  /             _________________                                        /                                               /             _________________                                     /          ______  
                 /             /          ______                                        /                                               /             /          ______                                     /  1615   \/ 8961   
                /   11        /  1615   \/ 8961                98                      /                                               /   11        /  1615   \/ 8961                98               9*3 /   ---- + --------  
               /    -- + 2*3 /   ---- + --------  + ------------------------          /                                               /    -- + 2*3 /   ---- + --------  + ------------------------      \/    108       12     
              /     3      \/    108       12              _________________         /                                               /     3      \/    108       12              _________________                             
             /                                            /          ______         /                                               /                                            /          ______                              
            /                                            /  1615   \/ 8961         /                                               /                                            /  1615   \/ 8961                               
           /                                        9*3 /   ---- + --------       /                                               /                                        9*3 /   ---- + --------                              
     1   \/                                           \/    108       12        \/                                              \/                                           \/    108       12                                 
x1 = - + -------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------
     2                                    2                                                                                                            2                                                                        
$$x_{1} = \frac{1}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}} - \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + \frac{14}{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}} + \frac{22}{3}}}{2} + \frac{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2}$$
                                                                                               _________________________________________________________________________________________________________________________________
                                                                                              /             _________________                                                                                                   
                                                                                             /             /          ______                                                                                                    
                                                                                            /   22        /  1615   \/ 8961                                      14                                               98            
                                                                                           /    -- - 2*3 /   ---- + --------  + -------------------------------------------------------------------- - ------------------------ 
                   __________________________________________________________             /     3      \/    108       12                 __________________________________________________________          _________________ 
                  /             _________________                                        /                                               /             _________________                                     /          ______  
                 /             /          ______                                        /                                               /             /          ______                                     /  1615   \/ 8961   
                /   11        /  1615   \/ 8961                98                      /                                               /   11        /  1615   \/ 8961                98               9*3 /   ---- + --------  
               /    -- + 2*3 /   ---- + --------  + ------------------------          /                                               /    -- + 2*3 /   ---- + --------  + ------------------------      \/    108       12     
              /     3      \/    108       12              _________________         /                                               /     3      \/    108       12              _________________                             
             /                                            /          ______         /                                               /                                            /          ______                              
            /                                            /  1615   \/ 8961         /                                               /                                            /  1615   \/ 8961                               
           /                                        9*3 /   ---- + --------       /                                               /                                        9*3 /   ---- + --------                              
     1   \/                                           \/    108       12        \/                                              \/                                           \/    108       12                                 
x2 = - + -------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------
     2                                    2                                                                                                            2                                                                        
$$x_{2} = - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}} - \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + \frac{14}{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}} + \frac{22}{3}}}{2} + \frac{1}{2} + \frac{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2}$$
                                                                                                 ___________________________________________________________________________________________________________________________________
                                                                                                /               _________________                                                                                                   
                                                                                               /               /          ______                                                                                                    
                                                                                              /     22        /  1615   \/ 8961                                      14                                               98            
                                                                                I*           /    - -- + 2*3 /   ---- + --------  + -------------------------------------------------------------------- + ------------------------ 
                   __________________________________________________________               /       3      \/    108       12                 __________________________________________________________          _________________ 
                  /             _________________                                          /                                                 /             _________________                                     /          ______  
                 /             /          ______                                          /                                                 /             /          ______                                     /  1615   \/ 8961   
                /   11        /  1615   \/ 8961                98                        /                                                 /   11        /  1615   \/ 8961                98               9*3 /   ---- + --------  
               /    -- + 2*3 /   ---- + --------  + ------------------------            /                                                 /    -- + 2*3 /   ---- + --------  + ------------------------      \/    108       12     
              /     3      \/    108       12              _________________           /                                                 /     3      \/    108       12              _________________                             
             /                                            /          ______           /                                                 /                                            /          ______                              
            /                                            /  1615   \/ 8961           /                                                 /                                            /  1615   \/ 8961                               
           /                                        9*3 /   ---- + --------         /                                                 /                                        9*3 /   ---- + --------                              
     1   \/                                           \/    108       12          \/                                                \/                                           \/    108       12                                 
x3 = - - -------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------
     2                                    2                                                                                                              2                                                                          
$$x_{3} = - \frac{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2} + \frac{1}{2} - \frac{i \sqrt{- \frac{22}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + \frac{14}{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2}$$
                                                                                                 ___________________________________________________________________________________________________________________________________
                                                                                                /               _________________                                                                                                   
                                                                                               /               /          ______                                                                                                    
                                                                                              /     22        /  1615   \/ 8961                                      14                                               98            
                                                                                I*           /    - -- + 2*3 /   ---- + --------  + -------------------------------------------------------------------- + ------------------------ 
                   __________________________________________________________               /       3      \/    108       12                 __________________________________________________________          _________________ 
                  /             _________________                                          /                                                 /             _________________                                     /          ______  
                 /             /          ______                                          /                                                 /             /          ______                                     /  1615   \/ 8961   
                /   11        /  1615   \/ 8961                98                        /                                                 /   11        /  1615   \/ 8961                98               9*3 /   ---- + --------  
               /    -- + 2*3 /   ---- + --------  + ------------------------            /                                                 /    -- + 2*3 /   ---- + --------  + ------------------------      \/    108       12     
              /     3      \/    108       12              _________________           /                                                 /     3      \/    108       12              _________________                             
             /                                            /          ______           /                                                 /                                            /          ______                              
            /                                            /  1615   \/ 8961           /                                                 /                                            /  1615   \/ 8961                               
           /                                        9*3 /   ---- + --------         /                                                 /                                        9*3 /   ---- + --------                              
     1   \/                                           \/    108       12          \/                                                \/                                           \/    108       12                                 
x4 = - - -------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------
     2                                    2                                                                                                              2                                                                          
$$x_{4} = - \frac{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2} + \frac{1}{2} + \frac{i \sqrt{- \frac{22}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + \frac{14}{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2}$$
x4 = -sqrt(11/3 + 98/(9*(sqrt(8961)/12 + 1615/108)^(1/3)) + 2*(sqrt(8961)/12 + 1615/108)^(1/3))/2 + 1/2 + i*sqrt(-22/3 + 98/(9*(sqrt(8961)/12 + 1615/108)^(1/3)) + 14/sqrt(11/3 + 98/(9*(sqrt(8961)/12 + 1615/108)^(1/3)) + 2*(sqrt(8961)/12 + 1615/108)^(1/3)) + 2*(sqrt(8961)/12 + 1615/108)^(1/3))/2
Suma y producto de raíces [src]
suma
                                                                                          _________________________________________________________________________________________________________________________________                                                                                             _________________________________________________________________________________________________________________________________                                                                                               ___________________________________________________________________________________________________________________________________                                                                                               ___________________________________________________________________________________________________________________________________
                                                                                         /             _________________                                                                                                                                                                                               /             _________________                                                                                                                                                                                                 /               _________________                                                                                                                                                                                                 /               _________________                                                                                                   
                                                                                        /             /          ______                                                                                                                                                                                               /             /          ______                                                                                                                                                                                                 /               /          ______                                                                                                                                                                                                 /               /          ______                                                                                                    
                                                                                       /   22        /  1615   \/ 8961                                      14                                               98                                                                                                      /   22        /  1615   \/ 8961                                      14                                               98                                                                                                        /     22        /  1615   \/ 8961                                      14                                               98                                                                                                        /     22        /  1615   \/ 8961                                      14                                               98            
                                                                                      /    -- - 2*3 /   ---- + --------  + -------------------------------------------------------------------- - ------------------------                                                                                          /    -- - 2*3 /   ---- + --------  + -------------------------------------------------------------------- - ------------------------                                                                               I*           /    - -- + 2*3 /   ---- + --------  + -------------------------------------------------------------------- + ------------------------                                                                               I*           /    - -- + 2*3 /   ---- + --------  + -------------------------------------------------------------------- + ------------------------ 
              __________________________________________________________             /     3      \/    108       12                 __________________________________________________________          _________________                  __________________________________________________________             /     3      \/    108       12                 __________________________________________________________          _________________                  __________________________________________________________               /       3      \/    108       12                 __________________________________________________________          _________________                  __________________________________________________________               /       3      \/    108       12                 __________________________________________________________          _________________ 
             /             _________________                                        /                                               /             _________________                                     /          ______                  /             _________________                                        /                                               /             _________________                                     /          ______                  /             _________________                                          /                                                 /             _________________                                     /          ______                  /             _________________                                          /                                                 /             _________________                                     /          ______  
            /             /          ______                                        /                                               /             /          ______                                     /  1615   \/ 8961                  /             /          ______                                        /                                               /             /          ______                                     /  1615   \/ 8961                  /             /          ______                                          /                                                 /             /          ______                                     /  1615   \/ 8961                  /             /          ______                                          /                                                 /             /          ______                                     /  1615   \/ 8961   
           /   11        /  1615   \/ 8961                98                      /                                               /   11        /  1615   \/ 8961                98               9*3 /   ---- + --------                /   11        /  1615   \/ 8961                98                      /                                               /   11        /  1615   \/ 8961                98               9*3 /   ---- + --------                /   11        /  1615   \/ 8961                98                        /                                                 /   11        /  1615   \/ 8961                98               9*3 /   ---- + --------                /   11        /  1615   \/ 8961                98                        /                                                 /   11        /  1615   \/ 8961                98               9*3 /   ---- + --------  
          /    -- + 2*3 /   ---- + --------  + ------------------------          /                                               /    -- + 2*3 /   ---- + --------  + ------------------------      \/    108       12                  /    -- + 2*3 /   ---- + --------  + ------------------------          /                                               /    -- + 2*3 /   ---- + --------  + ------------------------      \/    108       12                  /    -- + 2*3 /   ---- + --------  + ------------------------            /                                                 /    -- + 2*3 /   ---- + --------  + ------------------------      \/    108       12                  /    -- + 2*3 /   ---- + --------  + ------------------------            /                                                 /    -- + 2*3 /   ---- + --------  + ------------------------      \/    108       12     
         /     3      \/    108       12              _________________         /                                               /     3      \/    108       12              _________________                                         /     3      \/    108       12              _________________         /                                               /     3      \/    108       12              _________________                                         /     3      \/    108       12              _________________           /                                                 /     3      \/    108       12              _________________                                         /     3      \/    108       12              _________________           /                                                 /     3      \/    108       12              _________________                             
        /                                            /          ______         /                                               /                                            /          ______                                         /                                            /          ______         /                                               /                                            /          ______                                         /                                            /          ______           /                                                 /                                            /          ______                                         /                                            /          ______           /                                                 /                                            /          ______                              
       /                                            /  1615   \/ 8961         /                                               /                                            /  1615   \/ 8961                                         /                                            /  1615   \/ 8961         /                                               /                                            /  1615   \/ 8961                                         /                                            /  1615   \/ 8961           /                                                 /                                            /  1615   \/ 8961                                         /                                            /  1615   \/ 8961           /                                                 /                                            /  1615   \/ 8961                               
      /                                        9*3 /   ---- + --------       /                                               /                                        9*3 /   ---- + --------                                       /                                        9*3 /   ---- + --------       /                                               /                                        9*3 /   ---- + --------                                       /                                        9*3 /   ---- + --------         /                                                 /                                        9*3 /   ---- + --------                                       /                                        9*3 /   ---- + --------         /                                                 /                                        9*3 /   ---- + --------                              
1   \/                                           \/    108       12        \/                                              \/                                           \/    108       12                                    1   \/                                           \/    108       12        \/                                              \/                                           \/    108       12                                    1   \/                                           \/    108       12          \/                                                \/                                           \/    108       12                                    1   \/                                           \/    108       12          \/                                                \/                                           \/    108       12                                 
- + -------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------ + - + -------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------ + - - -------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------- + - - -------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------
2                                    2                                                                                                            2                                                                           2                                    2                                                                                                            2                                                                           2                                    2                                                                                                              2                                                                             2                                    2                                                                                                              2                                                                          
$$\left(\left(\left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}} - \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + \frac{14}{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}} + \frac{22}{3}}}{2} + \frac{1}{2} + \frac{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2}\right) + \left(\frac{1}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}} - \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + \frac{14}{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}} + \frac{22}{3}}}{2} + \frac{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2}\right)\right) + \left(- \frac{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2} + \frac{1}{2} - \frac{i \sqrt{- \frac{22}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + \frac{14}{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2}\right)\right) + \left(- \frac{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2} + \frac{1}{2} + \frac{i \sqrt{- \frac{22}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + \frac{14}{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2}\right)$$
=
2
$$2$$
producto
/                                                                                          _________________________________________________________________________________________________________________________________\ /                                                                                          _________________________________________________________________________________________________________________________________\ /                                                                                            ___________________________________________________________________________________________________________________________________\ /                                                                                            ___________________________________________________________________________________________________________________________________\
|                                                                                         /             _________________                                                                                                   | |                                                                                         /             _________________                                                                                                   | |                                                                                           /               _________________                                                                                                   | |                                                                                           /               _________________                                                                                                   |
|                                                                                        /             /          ______                                                                                                    | |                                                                                        /             /          ______                                                                                                    | |                                                                                          /               /          ______                                                                                                    | |                                                                                          /               /          ______                                                                                                    |
|                                                                                       /   22        /  1615   \/ 8961                                      14                                               98            | |                                                                                       /   22        /  1615   \/ 8961                                      14                                               98            | |                                                                                         /     22        /  1615   \/ 8961                                      14                                               98            | |                                                                                         /     22        /  1615   \/ 8961                                      14                                               98            |
|                                                                                      /    -- - 2*3 /   ---- + --------  + -------------------------------------------------------------------- - ------------------------ | |                                                                                      /    -- - 2*3 /   ---- + --------  + -------------------------------------------------------------------- - ------------------------ | |                                                                           I*           /    - -- + 2*3 /   ---- + --------  + -------------------------------------------------------------------- + ------------------------ | |                                                                           I*           /    - -- + 2*3 /   ---- + --------  + -------------------------------------------------------------------- + ------------------------ |
|              __________________________________________________________             /     3      \/    108       12                 __________________________________________________________          _________________ | |              __________________________________________________________             /     3      \/    108       12                 __________________________________________________________          _________________ | |              __________________________________________________________               /       3      \/    108       12                 __________________________________________________________          _________________ | |              __________________________________________________________               /       3      \/    108       12                 __________________________________________________________          _________________ |
|             /             _________________                                        /                                               /             _________________                                     /          ______  | |             /             _________________                                        /                                               /             _________________                                     /          ______  | |             /             _________________                                          /                                                 /             _________________                                     /          ______  | |             /             _________________                                          /                                                 /             _________________                                     /          ______  |
|            /             /          ______                                        /                                               /             /          ______                                     /  1615   \/ 8961   | |            /             /          ______                                        /                                               /             /          ______                                     /  1615   \/ 8961   | |            /             /          ______                                          /                                                 /             /          ______                                     /  1615   \/ 8961   | |            /             /          ______                                          /                                                 /             /          ______                                     /  1615   \/ 8961   |
|           /   11        /  1615   \/ 8961                98                      /                                               /   11        /  1615   \/ 8961                98               9*3 /   ---- + --------  | |           /   11        /  1615   \/ 8961                98                      /                                               /   11        /  1615   \/ 8961                98               9*3 /   ---- + --------  | |           /   11        /  1615   \/ 8961                98                        /                                                 /   11        /  1615   \/ 8961                98               9*3 /   ---- + --------  | |           /   11        /  1615   \/ 8961                98                        /                                                 /   11        /  1615   \/ 8961                98               9*3 /   ---- + --------  |
|          /    -- + 2*3 /   ---- + --------  + ------------------------          /                                               /    -- + 2*3 /   ---- + --------  + ------------------------      \/    108       12     | |          /    -- + 2*3 /   ---- + --------  + ------------------------          /                                               /    -- + 2*3 /   ---- + --------  + ------------------------      \/    108       12     | |          /    -- + 2*3 /   ---- + --------  + ------------------------            /                                                 /    -- + 2*3 /   ---- + --------  + ------------------------      \/    108       12     | |          /    -- + 2*3 /   ---- + --------  + ------------------------            /                                                 /    -- + 2*3 /   ---- + --------  + ------------------------      \/    108       12     |
|         /     3      \/    108       12              _________________         /                                               /     3      \/    108       12              _________________                             | |         /     3      \/    108       12              _________________         /                                               /     3      \/    108       12              _________________                             | |         /     3      \/    108       12              _________________           /                                                 /     3      \/    108       12              _________________                             | |         /     3      \/    108       12              _________________           /                                                 /     3      \/    108       12              _________________                             |
|        /                                            /          ______         /                                               /                                            /          ______                              | |        /                                            /          ______         /                                               /                                            /          ______                              | |        /                                            /          ______           /                                                 /                                            /          ______                              | |        /                                            /          ______           /                                                 /                                            /          ______                              |
|       /                                            /  1615   \/ 8961         /                                               /                                            /  1615   \/ 8961                               | |       /                                            /  1615   \/ 8961         /                                               /                                            /  1615   \/ 8961                               | |       /                                            /  1615   \/ 8961           /                                                 /                                            /  1615   \/ 8961                               | |       /                                            /  1615   \/ 8961           /                                                 /                                            /  1615   \/ 8961                               |
|      /                                        9*3 /   ---- + --------       /                                               /                                        9*3 /   ---- + --------                              | |      /                                        9*3 /   ---- + --------       /                                               /                                        9*3 /   ---- + --------                              | |      /                                        9*3 /   ---- + --------         /                                                 /                                        9*3 /   ---- + --------                              | |      /                                        9*3 /   ---- + --------         /                                                 /                                        9*3 /   ---- + --------                              |
|1   \/                                           \/    108       12        \/                                              \/                                           \/    108       12                                 | |1   \/                                           \/    108       12        \/                                              \/                                           \/    108       12                                 | |1   \/                                           \/    108       12          \/                                                \/                                           \/    108       12                                 | |1   \/                                           \/    108       12          \/                                                \/                                           \/    108       12                                 |
|- + -------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------|*|- + -------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------|*|- - -------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------|*|- - -------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------|
\2                                    2                                                                                                            2                                                                        / \2                                    2                                                                                                            2                                                                        / \2                                    2                                                                                                              2                                                                          / \2                                    2                                                                                                              2                                                                          /
$$\left(\frac{1}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}} - \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + \frac{14}{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}} + \frac{22}{3}}}{2} + \frac{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2}\right) \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}} - \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + \frac{14}{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}} + \frac{22}{3}}}{2} + \frac{1}{2} + \frac{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2}\right) \left(- \frac{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2} + \frac{1}{2} - \frac{i \sqrt{- \frac{22}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + \frac{14}{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2}\right) \left(- \frac{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2} + \frac{1}{2} + \frac{i \sqrt{- \frac{22}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + \frac{14}{\sqrt{\frac{11}{3} + \frac{98}{9 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}} + 2 \sqrt[3]{\frac{\sqrt{8961}}{12} + \frac{1615}{108}}}}{2}\right)$$
=
16
$$16$$
16
Respuesta numérica [src]
x1 = 2.96271542539271
x2 = 1.66758258378553
x3 = -1.31514900458912 + 1.22836235984099*i
x4 = -1.31514900458912 - 1.22836235984099*i
x4 = -1.31514900458912 - 1.22836235984099*i