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3+5x-(4x*(-4x)*(-4x)) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
3 + 5*x - 4*x*-4*x*-4*x = 0
−−4x−4x4x+(5x+3)=0- - 4 x - 4 x 4 x + \left(5 x + 3\right) = 0
Simplificar
Teorema de Cardano-Vieta
reescribamos la ecuación
−−4x−4x4x+(5x+3)=0- - 4 x - 4 x 4 x + \left(5 x + 3\right) = 0
de
ax3+bx2+cx+d=0a x^{3} + b x^{2} + c x + d = 0
como ecuación cúbica reducida
x3+bx2a+cxa+da=0x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0
x3−5x64−364=0x^{3} - \frac{5 x}{64} - \frac{3}{64} = 0
px2+qx+v+x3=0p x^{2} + q x + v + x^{3} = 0
donde
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=−564q = - \frac{5}{64}
v=dav = \frac{d}{a}
v=−364v = - \frac{3}{64}
Fórmulas de Cardano-Vieta
x1+x2+x3=−px_{1} + x_{2} + x_{3} = - p
x1x2+x1x3+x2x3=qx_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q
x1x2x3=vx_{1} x_{2} x_{3} = v
x1+x2+x3=0x_{1} + x_{2} + x_{3} = 0
x1x2+x1x3+x2x3=−564x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{5}{64}
x1x2x3=−364x_{1} x_{2} x_{3} = - \frac{3}{64}
Gráfica
-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.515.0-100000100000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
                                    _________________     /             _________________                             \                                       _________________     /           _________________                             \                                                      
                                   /         _______      |            /         _______                              |                                      /         _______      |          /         _______                              |                                                      
                                  /   3    \/ 11289       |    ___    /   3    \/ 11289                               |                                     /   3    \/ 11289       |  ___    /   3    \/ 11289                               |        _________________                             
                               3 /   --- + ---------      |  \/ 3 *3 /   --- + ---------                 ___          |                                  3 /   --- + ---------      |\/ 3 *3 /   --- + ---------                 ___          |       /         _______                              
              5                \/    128      4608        |        \/    128      4608               5*\/ 3           |                 5                \/    128      4608        |      \/    128      4608               5*\/ 3           |      /   3    \/ 11289                 5             
- -------------------------- - ---------------------- + I*|- ---------------------------- + --------------------------| + - -------------------------- - ---------------------- + I*|---------------------------- - --------------------------| + 3 /   --- + ---------  + --------------------------
           _________________             2                |               2                          _________________|              _________________             2                |             2                          _________________|   \/    128      4608               _________________
          /         _______                               |                                         /         _______ |             /         _______                               |                                       /         _______ |                                    /         _______ 
         /   3    \/ 11289                                |                                        /   3    \/ 11289  |            /   3    \/ 11289                                |                                      /   3    \/ 11289  |                                   /   3    \/ 11289  
  384*3 /   --- + ---------                               |                                 384*3 /   --- + --------- |     384*3 /   --- + ---------                               |                               384*3 /   --- + --------- |                            192*3 /   --- + --------- 
      \/    128      4608                                 \                                     \/    128      4608   /         \/    128      4608                                 \                                   \/    128      4608   /                                \/    128      4608
(5192112894608+31283+112894608+31283)+((−112894608+312832−5384112894608+31283+i(−3112894608+312832+53384112894608+31283))+(−112894608+312832−5384112894608+31283+i(−53384112894608+31283+3112894608+312832)))\left(\frac{5}{192 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}} + \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2} - \frac{5}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2} + \frac{5 \sqrt{3}}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2} - \frac{5}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}} + i \left(- \frac{5 \sqrt{3}}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2}\right)\right)\right) 
=
  /           _________________                             \     /             _________________                             \
  |          /         _______                              |     |            /         _______                              |
  |  ___    /   3    \/ 11289                               |     |    ___    /   3    \/ 11289                               |
  |\/ 3 *3 /   --- + ---------                 ___          |     |  \/ 3 *3 /   --- + ---------                 ___          |
  |      \/    128      4608               5*\/ 3           |     |        \/    128      4608               5*\/ 3           |
I*|---------------------------- - --------------------------| + I*|- ---------------------------- + --------------------------|
  |             2                          _________________|     |               2                          _________________|
  |                                       /         _______ |     |                                         /         _______ |
  |                                      /   3    \/ 11289  |     |                                        /   3    \/ 11289  |
  |                               384*3 /   --- + --------- |     |                                 384*3 /   --- + --------- |
  \                                   \/    128      4608   /     \                                     \/    128      4608   /
i(−3112894608+312832+53384112894608+31283)+i(−53384112894608+31283+3112894608+312832)i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2} + \frac{5 \sqrt{3}}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}\right) + i \left(- \frac{5 \sqrt{3}}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2}\right) 
producto
/                                    _________________     /             _________________                             \\ /                                    _________________     /           _________________                             \\                                                      
|                                   /         _______      |            /         _______                              || |                                   /         _______      |          /         _______                              ||                                                      
|                                  /   3    \/ 11289       |    ___    /   3    \/ 11289                               || |                                  /   3    \/ 11289       |  ___    /   3    \/ 11289                               || /     _________________                             \
|                               3 /   --- + ---------      |  \/ 3 *3 /   --- + ---------                 ___          || |                               3 /   --- + ---------      |\/ 3 *3 /   --- + ---------                 ___          || |    /         _______                              |
|              5                \/    128      4608        |        \/    128      4608               5*\/ 3           || |              5                \/    128      4608        |      \/    128      4608               5*\/ 3           || |   /   3    \/ 11289                 5             |
|- -------------------------- - ---------------------- + I*|- ---------------------------- + --------------------------||*|- -------------------------- - ---------------------- + I*|---------------------------- - --------------------------||*|3 /   --- + ---------  + --------------------------|
|           _________________             2                |               2                          _________________|| |           _________________             2                |             2                          _________________|| |\/    128      4608               _________________|
|          /         _______                               |                                         /         _______ || |          /         _______                               |                                       /         _______ || |                                 /         _______ |
|         /   3    \/ 11289                                |                                        /   3    \/ 11289  || |         /   3    \/ 11289                                |                                      /   3    \/ 11289  || |                                /   3    \/ 11289  |
|  384*3 /   --- + ---------                               |                                 384*3 /   --- + --------- || |  384*3 /   --- + ---------                               |                               384*3 /   --- + --------- || |                         192*3 /   --- + --------- |
\      \/    128      4608                                 \                                     \/    128      4608   // \      \/    128      4608                                 \                                   \/    128      4608   // \                             \/    128      4608   /
(−112894608+312832−5384112894608+31283+i(−53384112894608+31283+3112894608+312832))(−112894608+312832−5384112894608+31283+i(−3112894608+312832+53384112894608+31283))(5192112894608+31283+112894608+31283)\left(- \frac{\sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2} - \frac{5}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}} + i \left(- \frac{5 \sqrt{3}}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2} - \frac{5}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2} + \frac{5 \sqrt{3}}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}\right)\right) \left(\frac{5}{192 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}} + \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}\right) 
=
3/64
364\frac{3}{64} 
3/64
Respuesta rápida [src] 
                                         _________________     /             _________________                             \
                                        /         _______      |            /         _______                              |
                                       /   3    \/ 11289       |    ___    /   3    \/ 11289                               |
                                    3 /   --- + ---------      |  \/ 3 *3 /   --- + ---------                 ___          |
                   5                \/    128      4608        |        \/    128      4608               5*\/ 3           |
x1 = - -------------------------- - ---------------------- + I*|- ---------------------------- + --------------------------|
                _________________             2                |               2                          _________________|
               /         _______                               |                                         /         _______ |
              /   3    \/ 11289                                |                                        /   3    \/ 11289  |
       384*3 /   --- + ---------                               |                                 384*3 /   --- + --------- |
           \/    128      4608                                 \                                     \/    128      4608   /
x1=−112894608+312832−5384112894608+31283+i(−3112894608+312832+53384112894608+31283)x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2} - \frac{5}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2} + \frac{5 \sqrt{3}}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}\right) 
                                         _________________     /           _________________                             \
                                        /         _______      |          /         _______                              |
                                       /   3    \/ 11289       |  ___    /   3    \/ 11289                               |
                                    3 /   --- + ---------      |\/ 3 *3 /   --- + ---------                 ___          |
                   5                \/    128      4608        |      \/    128      4608               5*\/ 3           |
x2 = - -------------------------- - ---------------------- + I*|---------------------------- - --------------------------|
                _________________             2                |             2                          _________________|
               /         _______                               |                                       /         _______ |
              /   3    \/ 11289                                |                                      /   3    \/ 11289  |
       384*3 /   --- + ---------                               |                               384*3 /   --- + --------- |
           \/    128      4608                                 \                                   \/    128      4608   /
x2=−112894608+312832−5384112894608+31283+i(−53384112894608+31283+3112894608+312832)x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2} - \frac{5}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}} + i \left(- \frac{5 \sqrt{3}}{384 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}}{2}\right) 
          _________________                             
         /         _______                              
        /   3    \/ 11289                 5             
x3 = 3 /   --- + ---------  + --------------------------
     \/    128      4608               _________________
                                      /         _______ 
                                     /   3    \/ 11289  
                              192*3 /   --- + --------- 
                                  \/    128      4608
x3=5192112894608+31283+112894608+31283x_{3} = \frac{5}{192 \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}}} + \sqrt[3]{\frac{\sqrt{11289}}{4608} + \frac{3}{128}} 
x3 = 5/(192*(sqrt(11289)/4608 + 3/128)^(1/3)) + (sqrt(11289)/4608 + 3/128)^(1/3)
Respuesta numérica [src] 
x1 = 0.432007123934819
x2 = -0.216003561967409 - 0.248691809973359*i
x3 = -0.216003561967409 + 0.248691809973359*i
x3 = -0.216003561967409 + 0.248691809973359*i
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