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x^4-6x^2-3x-12=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
 4      2               
x  - 6*x  - 3*x - 12 = 0
$$\left(- 3 x + \left(x^{4} - 6 x^{2}\right)\right) - 12 = 0$$
Gráfica
Respuesta rápida [src]
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                                                                                               /                   6                    /    199   \/ 46513                                        6                                    
                                                                                 I*           /    -8 - ------------------------ + 2*3 /   - --- + ---------  + ----------------------------------------------------------------------- 
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              /   |               6                    /    199   \/ 46513  |             /             3 /   - --- + ---------                                        /   |               6                    /    199   \/ 46513  |  
             /    |4 - ------------------------ + 2*3 /   - --- + --------- |            /              \/       16       16                                          /    |4 - ------------------------ + 2*3 /   - --- + --------- |  
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       \/         |    \/       16       16                                 |      \/                                                                           \/         |    \/       16       16                                 |  
x1 = - ----------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------
                                          2                                                                                                                 2                                                                           
$$x_{1} = - \frac{\sqrt{\left|{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}\right|}}{2} - \frac{i \sqrt{-8 - \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + \frac{6}{\sqrt{\left|{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}\right|}}}}{2}$$
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                                                                                               /                   6                    /    199   \/ 46513                                        6                                    
                                                                                 I*           /    -8 - ------------------------ + 2*3 /   - --- + ---------  + ----------------------------------------------------------------------- 
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             /    |4 - ------------------------ + 2*3 /   - --- + --------- |            /              \/       16       16                                          /    |4 - ------------------------ + 2*3 /   - --- + --------- |  
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       \/         |    \/       16       16                                 |      \/                                                                           \/         |    \/       16       16                                 |  
x2 = - ----------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------
                                          2                                                                                                                 2                                                                           
$$x_{2} = - \frac{\sqrt{\left|{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}\right|}}{2} + \frac{i \sqrt{-8 - \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + \frac{6}{\sqrt{\left|{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}\right|}}}}{2}$$
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                                                                                         /            /    199   \/ 46513                6                                                 6                                   
                                                                                        /    8 - 2*3 /   - --- + ---------  + ------------------------ + --------------------------------------------------------------------- 
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            /                  6                    /    199   \/ 46513             /                                         3 /   - --- + ---------           /                  6                    /    199   \/ 46513    
           /    4 - ------------------------ + 2*3 /   - --- + ---------           /                                          \/       16       16             /    4 - ------------------------ + 2*3 /   - --- + ---------   
          /              ___________________     \/       16       16             /                                                                           /              ___________________     \/       16       16      
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       /            3 /   - --- + ---------                                    /                                                                           /            3 /   - --- + ---------                                
     \/             \/       16       16                                     \/                                                                          \/             \/       16       16                                   
x3 = --------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------
                                       2                                                                                                             2                                                                         
$$x_{3} = \frac{\sqrt{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 8 + \frac{6}{\sqrt{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}}}}{2}$$
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                                                                                         /            /    199   \/ 46513                6                                                 6                                   
                                                                                        /    8 - 2*3 /   - --- + ---------  + ------------------------ + --------------------------------------------------------------------- 
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            /                  6                    /    199   \/ 46513             /                                         3 /   - --- + ---------           /                  6                    /    199   \/ 46513    
           /    4 - ------------------------ + 2*3 /   - --- + ---------           /                                          \/       16       16             /    4 - ------------------------ + 2*3 /   - --- + ---------   
          /              ___________________     \/       16       16             /                                                                           /              ___________________     \/       16       16      
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       /            3 /   - --- + ---------                                    /                                                                           /            3 /   - --- + ---------                                
     \/             \/       16       16                                     \/                                                                          \/             \/       16       16                                   
x4 = --------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------
                                       2                                                                                                             2                                                                         
$$x_{4} = - \frac{\sqrt{- 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 8 + \frac{6}{\sqrt{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}}}}{2} + \frac{\sqrt{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}}{2}$$
x4 = -sqrt(-2*(-199/16 + sqrt(46513)/16)^(1/3) + 6/(-199/16 + sqrt(46513)/16)^(1/3) + 8 + 6/sqrt(-6/(-199/16 + sqrt(46513)/16)^(1/3) + 2*(-199/16 + sqrt(46513)/16)^(1/3) + 4))/2 + sqrt(-6/(-199/16 + sqrt(46513)/16)^(1/3) + 2*(-199/16 + sqrt(46513)/16)^(1/3) + 4)/2
Suma y producto de raíces [src]
suma
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                                                                                          /                   6                    /    199   \/ 46513                                        6                                                                                                                                 /                   6                    /    199   \/ 46513                                        6                                                                                                                           /            /    199   \/ 46513                6                                                 6                                                                                                                          /            /    199   \/ 46513                6                                                 6                                   
                                                                            I*           /    -8 - ------------------------ + 2*3 /   - --- + ---------  + -----------------------------------------------------------------------                                                                                I*           /    -8 - ------------------------ + 2*3 /   - --- + ---------  + -----------------------------------------------------------------------                                                                                       /    8 - 2*3 /   - --- + ---------  + ------------------------ + ---------------------------------------------------------------------                                                                                       /    8 - 2*3 /   - --- + ---------  + ------------------------ + --------------------------------------------------------------------- 
            _____________________________________________________________               /               ___________________     \/       16       16                 _____________________________________________________________                _____________________________________________________________               /               ___________________     \/       16       16                 _____________________________________________________________              ___________________________________________________________             /           \/       16       16            ___________________             ___________________________________________________________              ___________________________________________________________             /           \/       16       16            ___________________             ___________________________________________________________ 
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         /   |               6                    /    199   \/ 46513  |             /             3 /   - --- + ---------                                        /   |               6                    /    199   \/ 46513  |              /   |               6                    /    199   \/ 46513  |             /             3 /   - --- + ---------                                        /   |               6                    /    199   \/ 46513  |            /                  6                    /    199   \/ 46513             /                                         3 /   - --- + ---------           /                  6                    /    199   \/ 46513              /                  6                    /    199   \/ 46513             /                                         3 /   - --- + ---------           /                  6                    /    199   \/ 46513    
        /    |4 - ------------------------ + 2*3 /   - --- + --------- |            /              \/       16       16                                          /    |4 - ------------------------ + 2*3 /   - --- + --------- |             /    |4 - ------------------------ + 2*3 /   - --- + --------- |            /              \/       16       16                                          /    |4 - ------------------------ + 2*3 /   - --- + --------- |           /    4 - ------------------------ + 2*3 /   - --- + ---------           /                                          \/       16       16             /    4 - ------------------------ + 2*3 /   - --- + ---------            /    4 - ------------------------ + 2*3 /   - --- + ---------           /                                          \/       16       16             /    4 - ------------------------ + 2*3 /   - --- + ---------   
       /     |         ___________________     \/       16       16    |           /                                                                            /     |         ___________________     \/       16       16    |            /     |         ___________________     \/       16       16    |           /                                                                            /     |         ___________________     \/       16       16    |          /              ___________________     \/       16       16             /                                                                           /              ___________________     \/       16       16              /              ___________________     \/       16       16             /                                                                           /              ___________________     \/       16       16      
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    /        |    3 /   - --- + ---------                              |        /                                                                            /        |    3 /   - --- + ---------                              |         /        |    3 /   - --- + ---------                              |        /                                                                            /        |    3 /   - --- + ---------                              |       /            3 /   - --- + ---------                                    /                                                                           /            3 /   - --- + ---------                                     /            3 /   - --- + ---------                                    /                                                                           /            3 /   - --- + ---------                                
  \/         |    \/       16       16                                 |      \/                                                                           \/         |    \/       16       16                                 |       \/         |    \/       16       16                                 |      \/                                                                           \/         |    \/       16       16                                 |     \/             \/       16       16                                     \/                                                                          \/             \/       16       16                                      \/             \/       16       16                                     \/                                                                          \/             \/       16       16                                   
- ----------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------- + - ----------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------
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$$\left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 8 + \frac{6}{\sqrt{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}}}}{2} + \frac{\sqrt{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}}{2}\right) + \left(\left(\frac{\sqrt{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 8 + \frac{6}{\sqrt{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}}}}{2}\right) + \left(\left(- \frac{\sqrt{\left|{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}\right|}}{2} - \frac{i \sqrt{-8 - \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + \frac{6}{\sqrt{\left|{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}\right|}}}}{2}\right) + \left(- \frac{\sqrt{\left|{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}\right|}}{2} + \frac{i \sqrt{-8 - \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + \frac{6}{\sqrt{\left|{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}\right|}}}}{2}\right)\right)\right)$$
=
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       /                  6                    /    199   \/ 46513             /   |               6                    /    199   \/ 46513  | 
      /    4 - ------------------------ + 2*3 /   - --- + ---------   -       /    |4 - ------------------------ + 2*3 /   - --- + --------- | 
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\/             \/       16       16                                     \/         |    \/       16       16                                 | 
$$- \sqrt{\left|{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}\right|} + \sqrt{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}$$
producto
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|                                                                                          /                   6                    /    199   \/ 46513                                        6                                    | |                                                                                          /                   6                    /    199   \/ 46513                                        6                                    | |                                                                                    /            /    199   \/ 46513                6                                                 6                                   | |                                                                                    /            /    199   \/ 46513                6                                                 6                                   |
|                                                                            I*           /    -8 - ------------------------ + 2*3 /   - --- + ---------  + ----------------------------------------------------------------------- | |                                                                            I*           /    -8 - ------------------------ + 2*3 /   - --- + ---------  + ----------------------------------------------------------------------- | |                                                                                   /    8 - 2*3 /   - --- + ---------  + ------------------------ + --------------------------------------------------------------------- | |                                                                                   /    8 - 2*3 /   - --- + ---------  + ------------------------ + --------------------------------------------------------------------- |
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|         /   |               6                    /    199   \/ 46513  |             /             3 /   - --- + ---------                                        /   |               6                    /    199   \/ 46513  |  | |         /   |               6                    /    199   \/ 46513  |             /             3 /   - --- + ---------                                        /   |               6                    /    199   \/ 46513  |  | |       /                  6                    /    199   \/ 46513             /                                         3 /   - --- + ---------           /                  6                    /    199   \/ 46513    | |       /                  6                    /    199   \/ 46513             /                                         3 /   - --- + ---------           /                  6                    /    199   \/ 46513    |
|        /    |4 - ------------------------ + 2*3 /   - --- + --------- |            /              \/       16       16                                          /    |4 - ------------------------ + 2*3 /   - --- + --------- |  | |        /    |4 - ------------------------ + 2*3 /   - --- + --------- |            /              \/       16       16                                          /    |4 - ------------------------ + 2*3 /   - --- + --------- |  | |      /    4 - ------------------------ + 2*3 /   - --- + ---------           /                                          \/       16       16             /    4 - ------------------------ + 2*3 /   - --- + ---------   | |      /    4 - ------------------------ + 2*3 /   - --- + ---------           /                                          \/       16       16             /    4 - ------------------------ + 2*3 /   - --- + ---------   |
|       /     |         ___________________     \/       16       16    |           /                                                                            /     |         ___________________     \/       16       16    |  | |       /     |         ___________________     \/       16       16    |           /                                                                            /     |         ___________________     \/       16       16    |  | |     /              ___________________     \/       16       16             /                                                                           /              ___________________     \/       16       16      | |     /              ___________________     \/       16       16             /                                                                           /              ___________________     \/       16       16      |
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|    /        |    3 /   - --- + ---------                              |        /                                                                            /        |    3 /   - --- + ---------                              |  | |    /        |    3 /   - --- + ---------                              |        /                                                                            /        |    3 /   - --- + ---------                              |  | |  /            3 /   - --- + ---------                                    /                                                                           /            3 /   - --- + ---------                                | |  /            3 /   - --- + ---------                                    /                                                                           /            3 /   - --- + ---------                                |
|  \/         |    \/       16       16                                 |      \/                                                                           \/         |    \/       16       16                                 |  | |  \/         |    \/       16       16                                 |      \/                                                                           \/         |    \/       16       16                                 |  | |\/             \/       16       16                                     \/                                                                          \/             \/       16       16                                   | |\/             \/       16       16                                     \/                                                                          \/             \/       16       16                                   |
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$$\left(- \frac{\sqrt{\left|{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}\right|}}{2} - \frac{i \sqrt{-8 - \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + \frac{6}{\sqrt{\left|{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}\right|}}}}{2}\right) \left(- \frac{\sqrt{\left|{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}\right|}}{2} + \frac{i \sqrt{-8 - \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + \frac{6}{\sqrt{\left|{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}\right|}}}}{2}\right) \left(\frac{\sqrt{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 8 + \frac{6}{\sqrt{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}}}}{2}\right) \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 8 + \frac{6}{\sqrt{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}}}}{2} + \frac{\sqrt{- \frac{6}{\sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}}} + 2 \sqrt[3]{- \frac{199}{16} + \frac{\sqrt{46513}}{16}} + 4}}{2}\right)$$
=
-12
$$-12$$
-12
Respuesta numérica [src]
x1 = 2.90718919925062
x2 = -0.164938758128857 + 1.25472987917666*i
x3 = -2.57731168299291
x4 = -0.164938758128857 - 1.25472987917666*i
x4 = -0.164938758128857 - 1.25472987917666*i