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lg(3*x^2-2*x)=1-lg(x*2) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   /   2      \               
log\3*x  - 2*x/ = 1 - log(x*2)
$$\log{\left(3 x^{2} - 2 x \right)} = 1 - \log{\left(2 x \right)}$$
Gráfica
Respuesta rápida [src]
       /                          _________________________________________         /                _________________________________________ /                _________________________________________\\\         /                              _________________________________________\                   _________________________________________ /                _________________________________________\
       |                         /         _______________________                  |               /         _______________________          |               /         _______________________         |||         |                             /         _______________________         |                  /         _______________________          |               /         _______________________         |
       |    ___   3 ___   ___ 3 /         /                     2               ___ |      2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          |||     ___ |      ___     3 ___   ___ 3 /         /                     2          |         2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          |
       |  \/ 3    \/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E    \/ 3 *\- 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E //|   \/ 3 *\- 8*\/ 3  + 2*\/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /   - 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /
x1 = I*|- ----- + --------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------
       |    18                                72                                                                            _________________________________________                                      |                                         144                                                                                   _________________________________________                                  
       |                                                                                                                   /         _______________________                                               |                                                                                                                              /         _______________________                                           
       |                                                                                                                3 /         /                     2                                                |                                                                                                                           3 /         /                     2                                            
       \                                                                                                            144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                       /                                                                                                                       144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                   
$$x_{1} = - \frac{\sqrt{3} \left(- 8 \sqrt{3} + 2 \sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right)}{144} + \frac{- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}} + i \left(- \frac{\sqrt{3}}{18} + \frac{\sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{72} + \frac{\sqrt{3} \left(- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right)}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}\right)$$
       /                        _________________________________________         /                _________________________________________ /                _________________________________________\\\         /                            _________________________________________\                   _________________________________________ /                _________________________________________\
       |                       /         _______________________                  |               /         _______________________          |               /         _______________________         |||         |                           /         _______________________         |                  /         _______________________          |               /         _______________________         |
       |  ___   3 ___   ___ 3 /         /                     2               ___ |      2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          |||     ___ |    ___     3 ___   ___ 3 /         /                     2          |         2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          |
       |\/ 3    \/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E    \/ 3 *\- 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E //|   \/ 3 *\8*\/ 3  - 2*\/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /   - 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /
x2 = I*|----- - --------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------
       |  18                                72                                                                            _________________________________________                                      |                                        144                                                                                  _________________________________________                                  
       |                                                                                                                 /         _______________________                                               |                                                                                                                            /         _______________________                                           
       |                                                                                                              3 /         /                     2                                                |                                                                                                                         3 /         /                     2                                            
       \                                                                                                          144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                       /                                                                                                                     144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                   
$$x_{2} = \frac{\sqrt{3} \left(- 2 \sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}} + 8 \sqrt{3}\right)}{144} + \frac{- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}} + i \left(- \frac{\sqrt{3} \left(- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right)}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}} - \frac{\sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{72} + \frac{\sqrt{3}}{18}\right)$$
                  __________________________________________                                                  
         3 ___ 3 /                  ___   ____________  1/2                            2/3                    
     2   \/ 2 *\/  32 + 243*E + 9*\/ 3 *\/ 64 + 243*E *e                            4*2                       
x3 = - + --------------------------------------------------- + -----------------------------------------------
     9                            18                                __________________________________________
                                                                 3 /                  ___   ____________  1/2 
                                                               9*\/  32 + 243*E + 9*\/ 3 *\/ 64 + 243*E *e    
$$x_{3} = \frac{4 \cdot 2^{\frac{2}{3}}}{9 \sqrt[3]{32 + 243 e + 9 \sqrt{3} \sqrt{64 + 243 e} e^{\frac{1}{2}}}} + \frac{2}{9} + \frac{\sqrt[3]{2} \sqrt[3]{32 + 243 e + 9 \sqrt{3} \sqrt{64 + 243 e} e^{\frac{1}{2}}}}{18}$$
x3 = 4*2^(2/3)/(9*(32 + 243*E + 9*sqrt(3)*sqrt(64 + 243*E)*exp(1/2))^(1/3)) + 2/9 + 2^(1/3)*(32 + 243*E + 9*sqrt(3)*sqrt(64 + 243*E)*exp(1/2))^(1/3)/18
Suma y producto de raíces [src]
suma
  /                          _________________________________________         /                _________________________________________ /                _________________________________________\\\         /                              _________________________________________\                   _________________________________________ /                _________________________________________\     /                        _________________________________________         /                _________________________________________ /                _________________________________________\\\         /                            _________________________________________\                   _________________________________________ /                _________________________________________\                                                                                                            
  |                         /         _______________________                  |               /         _______________________          |               /         _______________________         |||         |                             /         _______________________         |                  /         _______________________          |               /         _______________________         |     |                       /         _______________________                  |               /         _______________________          |               /         _______________________         |||         |                           /         _______________________         |                  /         _______________________          |               /         _______________________         |                __________________________________________                                                  
  |    ___   3 ___   ___ 3 /         /                     2               ___ |      2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          |||     ___ |      ___     3 ___   ___ 3 /         /                     2          |         2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          |     |  ___   3 ___   ___ 3 /         /                     2               ___ |      2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          |||     ___ |    ___     3 ___   ___ 3 /         /                     2          |         2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          |       3 ___ 3 /                  ___   ____________  1/2                            2/3                    
  |  \/ 3    \/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E    \/ 3 *\- 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E //|   \/ 3 *\- 8*\/ 3  + 2*\/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /   - 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /     |\/ 3    \/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E    \/ 3 *\- 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E //|   \/ 3 *\8*\/ 3  - 2*\/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /   - 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /   2   \/ 2 *\/  32 + 243*E + 9*\/ 3 *\/ 64 + 243*E *e                            4*2                       
I*|- ----- + --------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------- + I*|----- - --------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------- + - + --------------------------------------------------- + -----------------------------------------------
  |    18                                72                                                                            _________________________________________                                      |                                         144                                                                                   _________________________________________                                       |  18                                72                                                                            _________________________________________                                      |                                        144                                                                                  _________________________________________                                     9                            18                                __________________________________________
  |                                                                                                                   /         _______________________                                               |                                                                                                                              /         _______________________                                                |                                                                                                                 /         _______________________                                               |                                                                                                                            /         _______________________                                                                                                          3 /                  ___   ____________  1/2 
  |                                                                                                                3 /         /                     2                                                |                                                                                                                           3 /         /                     2                                                 |                                                                                                              3 /         /                     2                                                |                                                                                                                         3 /         /                     2                                                                                                         9*\/  32 + 243*E + 9*\/ 3 *\/ 64 + 243*E *e    
  \                                                                                                            144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                       /                                                                                                                       144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                        \                                                                                                          144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                       /                                                                                                                     144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                                                                                                                               
$$\left(\frac{4 \cdot 2^{\frac{2}{3}}}{9 \sqrt[3]{32 + 243 e + 9 \sqrt{3} \sqrt{64 + 243 e} e^{\frac{1}{2}}}} + \frac{2}{9} + \frac{\sqrt[3]{2} \sqrt[3]{32 + 243 e + 9 \sqrt{3} \sqrt{64 + 243 e} e^{\frac{1}{2}}}}{18}\right) + \left(\left(\frac{\sqrt{3} \left(- 2 \sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}} + 8 \sqrt{3}\right)}{144} + \frac{- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}} + i \left(- \frac{\sqrt{3} \left(- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right)}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}} - \frac{\sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{72} + \frac{\sqrt{3}}{18}\right)\right) + \left(- \frac{\sqrt{3} \left(- 8 \sqrt{3} + 2 \sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right)}{144} + \frac{- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}} + i \left(- \frac{\sqrt{3}}{18} + \frac{\sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{72} + \frac{\sqrt{3} \left(- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right)}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}\right)\right)\right)$$
=
      /                          _________________________________________         /                _________________________________________ /                _________________________________________\\\     /                        _________________________________________         /                _________________________________________ /                _________________________________________\\\         /                              _________________________________________\                                                                         _________________________________________ /                _________________________________________\         /                            _________________________________________\                                                  
      |                         /         _______________________                  |               /         _______________________          |               /         _______________________         |||     |                       /         _______________________                  |               /         _______________________          |               /         _______________________         |||         |                             /         _______________________         |            __________________________________________                  /         _______________________          |               /         _______________________         |         |                           /         _______________________         |                                                  
      |    ___   3 ___   ___ 3 /         /                     2               ___ |      2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          |||     |  ___   3 ___   ___ 3 /         /                     2               ___ |      2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          |||     ___ |      ___     3 ___   ___ 3 /         /                     2          |   3 ___ 3 /                  ___   ____________  1/2          2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          |     ___ |    ___     3 ___   ___ 3 /         /                     2          |                           2/3                    
2     |  \/ 3    \/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E    \/ 3 *\- 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E //|     |\/ 3    \/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E    \/ 3 *\- 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E //|   \/ 3 *\- 8*\/ 3  + 2*\/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /   \/ 2 *\/  32 + 243*E + 9*\/ 3 *\/ 64 + 243*E *e       - 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /   \/ 3 *\8*\/ 3  - 2*\/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /                        4*2                       
- + I*|- ----- + --------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------| + I*|----- - --------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------- + --------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------- + -----------------------------------------------
9     |    18                                72                                                                            _________________________________________                                      |     |  18                                72                                                                            _________________________________________                                      |                                         144                                                                  18                                                                     _________________________________________                                                                          144                                             __________________________________________
      |                                                                                                                   /         _______________________                                               |     |                                                                                                                 /         _______________________                                               |                                                                                                                                                                                    /         _______________________                                                                                                                                3 /                  ___   ____________  1/2 
      |                                                                                                                3 /         /                     2                                                |     |                                                                                                              3 /         /                     2                                                |                                                                                                                                                                                 3 /         /                     2                                                                                                                               9*\/  32 + 243*E + 9*\/ 3 *\/ 64 + 243*E *e    
      \                                                                                                            144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                       /     \                                                                                                          144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                       /                                                                                                                                                                              72*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                                                                                                                                                     
$$- \frac{\sqrt{3} \left(- 8 \sqrt{3} + 2 \sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right)}{144} + \frac{\sqrt{3} \left(- 2 \sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}} + 8 \sqrt{3}\right)}{144} + \frac{4 \cdot 2^{\frac{2}{3}}}{9 \sqrt[3]{32 + 243 e + 9 \sqrt{3} \sqrt{64 + 243 e} e^{\frac{1}{2}}}} + \frac{2}{9} + \frac{- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{72 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}} + \frac{\sqrt[3]{2} \sqrt[3]{32 + 243 e + 9 \sqrt{3} \sqrt{64 + 243 e} e^{\frac{1}{2}}}}{18} + i \left(- \frac{\sqrt{3} \left(- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right)}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}} - \frac{\sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{72} + \frac{\sqrt{3}}{18}\right) + i \left(- \frac{\sqrt{3}}{18} + \frac{\sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{72} + \frac{\sqrt{3} \left(- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right)}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}\right)$$
producto
/  /                          _________________________________________         /                _________________________________________ /                _________________________________________\\\         /                              _________________________________________\                   _________________________________________ /                _________________________________________\\ /  /                        _________________________________________         /                _________________________________________ /                _________________________________________\\\         /                            _________________________________________\                   _________________________________________ /                _________________________________________\\                                                                                                            
|  |                         /         _______________________                  |               /         _______________________          |               /         _______________________         |||         |                             /         _______________________         |                  /         _______________________          |               /         _______________________         || |  |                       /         _______________________                  |               /         _______________________          |               /         _______________________         |||         |                           /         _______________________         |                  /         _______________________          |               /         _______________________         || /             __________________________________________                                                  \
|  |    ___   3 ___   ___ 3 /         /                     2               ___ |      2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          |||     ___ |      ___     3 ___   ___ 3 /         /                     2          |         2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          || |  |  ___   3 ___   ___ 3 /         /                     2               ___ |      2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          |||     ___ |    ___     3 ___   ___ 3 /         /                     2          |         2/3   3 /         /                     2           |      3 ___ 3 /         /                     2          || |    3 ___ 3 /                  ___   ____________  1/2                            2/3                    |
|  |  \/ 3    \/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E    \/ 3 *\- 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E //|   \/ 3 *\- 8*\/ 3  + 2*\/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /   - 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /| |  |\/ 3    \/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E    \/ 3 *\- 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E //|   \/ 3 *\8*\/ 3  - 2*\/ 2 *\/ 3 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /   - 32*2    + \/   32 + \/  -1024 + (32 + 243*E)   + 243*E *\8 + 2*\/ 2 *\/   32 + \/  -1024 + (32 + 243*E)   + 243*E /| |2   \/ 2 *\/  32 + 243*E + 9*\/ 3 *\/ 64 + 243*E *e                            4*2                       |
|I*|- ----- + --------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------|*|I*|----- - --------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------|*|- + --------------------------------------------------- + -----------------------------------------------|
|  |    18                                72                                                                            _________________________________________                                      |                                         144                                                                                   _________________________________________                                  | |  |  18                                72                                                                            _________________________________________                                      |                                        144                                                                                  _________________________________________                                  | |9                            18                                __________________________________________|
|  |                                                                                                                   /         _______________________                                               |                                                                                                                              /         _______________________                                           | |  |                                                                                                                 /         _______________________                                               |                                                                                                                            /         _______________________                                           | |                                                            3 /                  ___   ____________  1/2 |
|  |                                                                                                                3 /         /                     2                                                |                                                                                                                           3 /         /                     2                                            | |  |                                                                                                              3 /         /                     2                                                |                                                                                                                         3 /         /                     2                                            | \                                                          9*\/  32 + 243*E + 9*\/ 3 *\/ 64 + 243*E *e    /
\  \                                                                                                            144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                       /                                                                                                                       144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                   / \  \                                                                                                          144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                       /                                                                                                                     144*\/   32 + \/  -1024 + (32 + 243*E)   + 243*E                                   /                                                                                                            
$$\left(- \frac{\sqrt{3} \left(- 8 \sqrt{3} + 2 \sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right)}{144} + \frac{- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}} + i \left(- \frac{\sqrt{3}}{18} + \frac{\sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{72} + \frac{\sqrt{3} \left(- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right)}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}\right)\right) \left(\frac{\sqrt{3} \left(- 2 \sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}} + 8 \sqrt{3}\right)}{144} + \frac{- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}} + i \left(- \frac{\sqrt{3} \left(- 32 \cdot 2^{\frac{2}{3}} + \left(8 + 2 \sqrt[3]{2} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right) \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}\right)}{144 \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}} - \frac{\sqrt[3]{2} \sqrt{3} \sqrt[3]{32 + 243 e + \sqrt{-1024 + \left(32 + 243 e\right)^{2}}}}{72} + \frac{\sqrt{3}}{18}\right)\right) \left(\frac{4 \cdot 2^{\frac{2}{3}}}{9 \sqrt[3]{32 + 243 e + 9 \sqrt{3} \sqrt{64 + 243 e} e^{\frac{1}{2}}}} + \frac{2}{9} + \frac{\sqrt[3]{2} \sqrt[3]{32 + 243 e + 9 \sqrt{3} \sqrt{64 + 243 e} e^{\frac{1}{2}}}}{18}\right)$$
=
            2       ___   ____________  3/2 
32*E + 243*e  + 9*\/ 3 *\/ 64 + 243*E *e    
--------------------------------------------
  /                 ___   ____________  1/2\
6*\32 + 243*E + 9*\/ 3 *\/ 64 + 243*E *e   /
$$\frac{32 e + 243 e^{2} + 9 \sqrt{3} \sqrt{64 + 243 e} e^{\frac{3}{2}}}{6 \left(32 + 243 e + 9 \sqrt{3} \sqrt{64 + 243 e} e^{\frac{1}{2}}\right)}$$
(32*E + 243*exp(2) + 9*sqrt(3)*sqrt(64 + 243*E)*exp(3/2))/(6*(32 + 243*E + 9*sqrt(3)*sqrt(64 + 243*E)*exp(1/2)))
Respuesta numérica [src]
x1 = -0.199480976137646 + 0.620767762027539*i
x2 = -0.199480976137646 - 0.620767762027539*i
x3 = 1.06562861894196
x3 = 1.06562861894196