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(x^3+6*x^2-15*x+12)/(4*sqrt(1-x)*(1-x)*(1+x)^3)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
    3      2                    
   x  + 6*x  - 15*x + 12        
---------------------------- = 0
    _______                3    
4*\/ 1 - x *(1 - x)*(1 + x)     
$$\frac{\left(- 15 x + \left(x^{3} + 6 x^{2}\right)\right) + 12}{4 \sqrt{1 - x} \left(1 - x\right) \left(x + 1\right)^{3}} = 0$$
Gráfica
Respuesta rápida [src]
             _________________                              /                                    _________________\
          3 /             ___                               |              ___            ___ 3 /             ___ |
          \/  783 + 108*\/ 7               27               |         27*\/ 3           \/ 3 *\/  783 + 108*\/ 7  |
x1 = -2 + -------------------- + ---------------------- + I*|- ---------------------- + --------------------------|
                   6                  _________________     |       _________________               6             |
                                   3 /             ___      |    3 /             ___                              |
                                 2*\/  783 + 108*\/ 7       \  2*\/  783 + 108*\/ 7                               /
$$x_{1} = -2 + \frac{27}{2 \sqrt[3]{108 \sqrt{7} + 783}} + \frac{\sqrt[3]{108 \sqrt{7} + 783}}{6} + i \left(- \frac{27 \sqrt{3}}{2 \sqrt[3]{108 \sqrt{7} + 783}} + \frac{\sqrt{3} \sqrt[3]{108 \sqrt{7} + 783}}{6}\right)$$
             _________________                              /           _________________                         \
          3 /             ___                               |    ___ 3 /             ___                ___       |
          \/  783 + 108*\/ 7               27               |  \/ 3 *\/  783 + 108*\/ 7            27*\/ 3        |
x2 = -2 + -------------------- + ---------------------- + I*|- -------------------------- + ----------------------|
                   6                  _________________     |              6                     _________________|
                                   3 /             ___      |                                 3 /             ___ |
                                 2*\/  783 + 108*\/ 7       \                               2*\/  783 + 108*\/ 7  /
$$x_{2} = -2 + \frac{27}{2 \sqrt[3]{108 \sqrt{7} + 783}} + \frac{\sqrt[3]{108 \sqrt{7} + 783}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{108 \sqrt{7} + 783}}{6} + \frac{27 \sqrt{3}}{2 \sqrt[3]{108 \sqrt{7} + 783}}\right)$$
                                    _________________
                                 3 /             ___ 
                   27            \/  783 + 108*\/ 7  
x3 = -2 - -------------------- - --------------------
             _________________            3          
          3 /             ___                        
          \/  783 + 108*\/ 7                         
$$x_{3} = - \frac{\sqrt[3]{108 \sqrt{7} + 783}}{3} - \frac{27}{\sqrt[3]{108 \sqrt{7} + 783}} - 2$$
x3 = -(108*sqrt(7) + 783)^(1/3)/3 - 27/(108*sqrt(7) + 783)^(1/3) - 2
Suma y producto de raíces [src]
suma
        _________________                              /                                    _________________\           _________________                              /           _________________                         \                                  _________________
     3 /             ___                               |              ___            ___ 3 /             ___ |        3 /             ___                               |    ___ 3 /             ___                ___       |                               3 /             ___ 
     \/  783 + 108*\/ 7               27               |         27*\/ 3           \/ 3 *\/  783 + 108*\/ 7  |        \/  783 + 108*\/ 7               27               |  \/ 3 *\/  783 + 108*\/ 7            27*\/ 3        |                 27            \/  783 + 108*\/ 7  
-2 + -------------------- + ---------------------- + I*|- ---------------------- + --------------------------| + -2 + -------------------- + ---------------------- + I*|- -------------------------- + ----------------------| + -2 - -------------------- - --------------------
              6                  _________________     |       _________________               6             |                 6                  _________________     |              6                     _________________|           _________________            3          
                              3 /             ___      |    3 /             ___                              |                                 3 /             ___      |                                 3 /             ___ |        3 /             ___                        
                            2*\/  783 + 108*\/ 7       \  2*\/  783 + 108*\/ 7                               /                               2*\/  783 + 108*\/ 7       \                               2*\/  783 + 108*\/ 7  /        \/  783 + 108*\/ 7                         
$$\left(- \frac{\sqrt[3]{108 \sqrt{7} + 783}}{3} - \frac{27}{\sqrt[3]{108 \sqrt{7} + 783}} - 2\right) + \left(\left(-2 + \frac{27}{2 \sqrt[3]{108 \sqrt{7} + 783}} + \frac{\sqrt[3]{108 \sqrt{7} + 783}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{108 \sqrt{7} + 783}}{6} + \frac{27 \sqrt{3}}{2 \sqrt[3]{108 \sqrt{7} + 783}}\right)\right) + \left(-2 + \frac{27}{2 \sqrt[3]{108 \sqrt{7} + 783}} + \frac{\sqrt[3]{108 \sqrt{7} + 783}}{6} + i \left(- \frac{27 \sqrt{3}}{2 \sqrt[3]{108 \sqrt{7} + 783}} + \frac{\sqrt{3} \sqrt[3]{108 \sqrt{7} + 783}}{6}\right)\right)\right)$$
=
       /                                    _________________\     /           _________________                         \
       |              ___            ___ 3 /             ___ |     |    ___ 3 /             ___                ___       |
       |         27*\/ 3           \/ 3 *\/  783 + 108*\/ 7  |     |  \/ 3 *\/  783 + 108*\/ 7            27*\/ 3        |
-6 + I*|- ---------------------- + --------------------------| + I*|- -------------------------- + ----------------------|
       |       _________________               6             |     |              6                     _________________|
       |    3 /             ___                              |     |                                 3 /             ___ |
       \  2*\/  783 + 108*\/ 7                               /     \                               2*\/  783 + 108*\/ 7  /
$$-6 + i \left(- \frac{\sqrt{3} \sqrt[3]{108 \sqrt{7} + 783}}{6} + \frac{27 \sqrt{3}}{2 \sqrt[3]{108 \sqrt{7} + 783}}\right) + i \left(- \frac{27 \sqrt{3}}{2 \sqrt[3]{108 \sqrt{7} + 783}} + \frac{\sqrt{3} \sqrt[3]{108 \sqrt{7} + 783}}{6}\right)$$
producto
/        _________________                              /                                    _________________\\ /        _________________                              /           _________________                         \\ /                               _________________\
|     3 /             ___                               |              ___            ___ 3 /             ___ || |     3 /             ___                               |    ___ 3 /             ___                ___       || |                            3 /             ___ |
|     \/  783 + 108*\/ 7               27               |         27*\/ 3           \/ 3 *\/  783 + 108*\/ 7  || |     \/  783 + 108*\/ 7               27               |  \/ 3 *\/  783 + 108*\/ 7            27*\/ 3        || |              27            \/  783 + 108*\/ 7  |
|-2 + -------------------- + ---------------------- + I*|- ---------------------- + --------------------------||*|-2 + -------------------- + ---------------------- + I*|- -------------------------- + ----------------------||*|-2 - -------------------- - --------------------|
|              6                  _________________     |       _________________               6             || |              6                  _________________     |              6                     _________________|| |        _________________            3          |
|                              3 /             ___      |    3 /             ___                              || |                              3 /             ___      |                                 3 /             ___ || |     3 /             ___                        |
\                            2*\/  783 + 108*\/ 7       \  2*\/  783 + 108*\/ 7                               // \                            2*\/  783 + 108*\/ 7       \                               2*\/  783 + 108*\/ 7  // \     \/  783 + 108*\/ 7                         /
$$\left(-2 + \frac{27}{2 \sqrt[3]{108 \sqrt{7} + 783}} + \frac{\sqrt[3]{108 \sqrt{7} + 783}}{6} + i \left(- \frac{27 \sqrt{3}}{2 \sqrt[3]{108 \sqrt{7} + 783}} + \frac{\sqrt{3} \sqrt[3]{108 \sqrt{7} + 783}}{6}\right)\right) \left(-2 + \frac{27}{2 \sqrt[3]{108 \sqrt{7} + 783}} + \frac{\sqrt[3]{108 \sqrt{7} + 783}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{108 \sqrt{7} + 783}}{6} + \frac{27 \sqrt{3}}{2 \sqrt[3]{108 \sqrt{7} + 783}}\right)\right) \left(- \frac{\sqrt[3]{108 \sqrt{7} + 783}}{3} - \frac{27}{\sqrt[3]{108 \sqrt{7} + 783}} - 2\right)$$
=
-12
$$-12$$
-12
Respuesta numérica [src]
x1 = 1.02442548101492 + 0.664415886803518*i
x2 = 1.02442548101492 - 0.664415886803518*i
x3 = -8.04885096202983
x3 = -8.04885096202983