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x^3-x-3=0

x^3-x-3=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
 3            
x  - x - 3 = 0
(x3−x)−3=0\left(x^{3} - x\right) - 3 = 0
Simplificar
Teorema de Cardano-Vieta
es ecuación cúbica reducida
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=−1q = -1
v=dav = \frac{d}{a}
v=−3v = -3
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=−1x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -1
x1x2x3=−3x_{1} x_{2} x_{3} = -3
Gráfica
-10.0-7.5-5.0-2.50.02.55.07.510.012.515.017.5-25002500
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
            _____________                            /             _____________                       \
           /       _____                             |            /       _____                        |
          /  3   \/ 717                              |    ___    /  3   \/ 717                         |
       3 /   - + -------                             |  \/ 3 *3 /   - + -------             ___        |
       \/    2      18               1               |        \/    2      18             \/ 3         |
x1 = - ------------------ - -------------------- + I*|- ------------------------ + --------------------|
               2                   _____________     |             2                      _____________|
                                  /       _____      |                                   /       _____ |
                                 /  3   \/ 717       |                                  /  3   \/ 717  |
                            6*3 /   - + -------      |                             6*3 /   - + ------- |
                              \/    2      18        \                               \/    2      18   /
x1=−71718+3232−1671718+323+i(−371718+3232+3671718+323)x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2} + \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}\right) 
            _____________                            /           _____________                       \
           /       _____                             |          /       _____                        |
          /  3   \/ 717                              |  ___    /  3   \/ 717                         |
       3 /   - + -------                             |\/ 3 *3 /   - + -------             ___        |
       \/    2      18               1               |      \/    2      18             \/ 3         |
x2 = - ------------------ - -------------------- + I*|------------------------ - --------------------|
               2                   _____________     |           2                      _____________|
                                  /       _____      |                                 /       _____ |
                                 /  3   \/ 717       |                                /  3   \/ 717  |
                            6*3 /   - + -------      |                           6*3 /   - + ------- |
                              \/    2      18        \                             \/    2      18   /
x2=−71718+3232−1671718+323+i(−3671718+323+371718+3232)x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}} + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2}\right) 
          _____________                       
         /       _____                        
        /  3   \/ 717              1          
x3 = 3 /   - + -------  + --------------------
     \/    2      18             _____________
                                /       _____ 
                               /  3   \/ 717  
                          3*3 /   - + ------- 
                            \/    2      18
x3=1371718+323+71718+323x_{3} = \frac{1}{3 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}} + \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}} 
x3 = 1/(3*(sqrt(717)/18 + 3/2)^(1/3)) + (sqrt(717)/18 + 3/2)^(1/3)
Suma y producto de raíces [src] 
suma
       _____________                            /             _____________                       \          _____________                            /           _____________                       \                                            
      /       _____                             |            /       _____                        |         /       _____                             |          /       _____                        |                                            
     /  3   \/ 717                              |    ___    /  3   \/ 717                         |        /  3   \/ 717                              |  ___    /  3   \/ 717                         |        _____________                       
  3 /   - + -------                             |  \/ 3 *3 /   - + -------             ___        |     3 /   - + -------                             |\/ 3 *3 /   - + -------             ___        |       /       _____                        
  \/    2      18               1               |        \/    2      18             \/ 3         |     \/    2      18               1               |      \/    2      18             \/ 3         |      /  3   \/ 717              1          
- ------------------ - -------------------- + I*|- ------------------------ + --------------------| + - ------------------ - -------------------- + I*|------------------------ - --------------------| + 3 /   - + -------  + --------------------
          2                   _____________     |             2                      _____________|             2                   _____________     |           2                      _____________|   \/    2      18             _____________
                             /       _____      |                                   /       _____ |                                /       _____      |                                 /       _____ |                              /       _____ 
                            /  3   \/ 717       |                                  /  3   \/ 717  |                               /  3   \/ 717       |                                /  3   \/ 717  |                             /  3   \/ 717  
                       6*3 /   - + -------      |                             6*3 /   - + ------- |                          6*3 /   - + -------      |                           6*3 /   - + ------- |                        3*3 /   - + ------- 
                         \/    2      18        \                               \/    2      18   /                            \/    2      18        \                             \/    2      18   /                          \/    2      18
(1371718+323+71718+323)+((−71718+3232−1671718+323+i(−371718+3232+3671718+323))+(−71718+3232−1671718+323+i(−3671718+323+371718+3232)))\left(\frac{1}{3 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}} + \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2} + \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}} + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2}\right)\right)\right) 
=
  /           _____________                       \     /             _____________                       \
  |          /       _____                        |     |            /       _____                        |
  |  ___    /  3   \/ 717                         |     |    ___    /  3   \/ 717                         |
  |\/ 3 *3 /   - + -------             ___        |     |  \/ 3 *3 /   - + -------             ___        |
  |      \/    2      18             \/ 3         |     |        \/    2      18             \/ 3         |
I*|------------------------ - --------------------| + I*|- ------------------------ + --------------------|
  |           2                      _____________|     |             2                      _____________|
  |                                 /       _____ |     |                                   /       _____ |
  |                                /  3   \/ 717  |     |                                  /  3   \/ 717  |
  |                           6*3 /   - + ------- |     |                             6*3 /   - + ------- |
  \                             \/    2      18   /     \                               \/    2      18   /
i(−371718+3232+3671718+323)+i(−3671718+323+371718+3232)i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2} + \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}\right) + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2}\right) 
producto
/       _____________                            /             _____________                       \\ /       _____________                            /           _____________                       \\                                            
|      /       _____                             |            /       _____                        || |      /       _____                             |          /       _____                        ||                                            
|     /  3   \/ 717                              |    ___    /  3   \/ 717                         || |     /  3   \/ 717                              |  ___    /  3   \/ 717                         || /     _____________                       \
|  3 /   - + -------                             |  \/ 3 *3 /   - + -------             ___        || |  3 /   - + -------                             |\/ 3 *3 /   - + -------             ___        || |    /       _____                        |
|  \/    2      18               1               |        \/    2      18             \/ 3         || |  \/    2      18               1               |      \/    2      18             \/ 3         || |   /  3   \/ 717              1          |
|- ------------------ - -------------------- + I*|- ------------------------ + --------------------||*|- ------------------ - -------------------- + I*|------------------------ - --------------------||*|3 /   - + -------  + --------------------|
|          2                   _____________     |             2                      _____________|| |          2                   _____________     |           2                      _____________|| |\/    2      18             _____________|
|                             /       _____      |                                   /       _____ || |                             /       _____      |                                 /       _____ || |                           /       _____ |
|                            /  3   \/ 717       |                                  /  3   \/ 717  || |                            /  3   \/ 717       |                                /  3   \/ 717  || |                          /  3   \/ 717  |
|                       6*3 /   - + -------      |                             6*3 /   - + ------- || |                       6*3 /   - + -------      |                           6*3 /   - + ------- || |                     3*3 /   - + ------- |
\                         \/    2      18        \                               \/    2      18   // \                         \/    2      18        \                             \/    2      18   // \                       \/    2      18   /
(−71718+3232−1671718+323+i(−3671718+323+371718+3232))(−71718+3232−1671718+323+i(−371718+3232+3671718+323))(1371718+323+71718+323)\left(- \frac{\sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}} + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}{2} + \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}}\right)\right) \left(\frac{1}{3 \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}} + \sqrt[3]{\frac{\sqrt{717}}{18} + \frac{3}{2}}\right) 
=
3
33 
3
Respuesta numérica [src] 
x1 = 1.67169988165716
x2 = -0.83584994082858 - 1.04686931884998*i
x3 = -0.83584994082858 + 1.04686931884998*i
x3 = -0.83584994082858 + 1.04686931884998*i
Gráfico
x^3-x-3=0 la ecuación
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