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x^5-33x^2*sqrt(x)+32=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
 5       2   ___         
x  - 33*x *\/ x  + 32 = 0
(−x33x2+x5)+32=0\left(- \sqrt{x} 33 x^{2} + x^{5}\right) + 32 = 0
Simplificar
Gráfica
402-12-10-8-6-4-2-5050
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
                                                                                                         ___________                        ___________
                                ___________                           ___________           ___         /       ___            ___         /       ___ 
               ___       ___   /       ___           ___       ___   /       ___      1   \/ 5         /  5   \/ 5       1   \/ 5         /  5   \/ 5  
1 + 4 + -1 - \/ 5  - I*\/ 2 *\/  5 - \/ 5   + -1 - \/ 5  + I*\/ 2 *\/  5 - \/ 5   + - - - ----- - I*  /   - - -----  + - - - ----- + I*  /   - - ----- 
                                                                                      4     4       \/    8     8        4     4       \/    8     8
((−54−14−i58−58)+(((1+4)+(−5−1−2i5−5))+(−5−1+2i5−5)))+(−54−14+i58−58)\left(\left(- \frac{\sqrt{5}}{4} - \frac{1}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right) + \left(\left(\left(1 + 4\right) + \left(- \sqrt{5} - 1 - \sqrt{2} i \sqrt{5 - \sqrt{5}}\right)\right) + \left(- \sqrt{5} - 1 + \sqrt{2} i \sqrt{5 - \sqrt{5}}\right)\right)\right) + \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right) 
=
        ___
5   5*\/ 5 
- - -------
2      2
52−552\frac{5}{2} - \frac{5 \sqrt{5}}{2} 
producto
                                                                              /                     ___________\ /                     ___________\
  /                        ___________\ /                        ___________\ |        ___         /       ___ | |        ___         /       ___ |
  |       ___       ___   /       ___ | |       ___       ___   /       ___ | |  1   \/ 5         /  5   \/ 5  | |  1   \/ 5         /  5   \/ 5  |
4*\-1 - \/ 5  - I*\/ 2 *\/  5 - \/ 5  /*\-1 - \/ 5  + I*\/ 2 *\/  5 - \/ 5  /*|- - - ----- - I*  /   - - ----- |*|- - - ----- + I*  /   - - ----- |
                                                                              \  4     4       \/    8     8   / \  4     4       \/    8     8   /
4(−5−1−2i5−5)(−5−1+2i5−5)(−54−14−i58−58)(−54−14+i58−58)4 \left(- \sqrt{5} - 1 - \sqrt{2} i \sqrt{5 - \sqrt{5}}\right) \left(- \sqrt{5} - 1 + \sqrt{2} i \sqrt{5 - \sqrt{5}}\right) \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right) \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right) 
=
                                   2                                     2
/                     ____________\  /                       ___________\ 
|      ___     ___   /        ___ |  |      ___       ___   /       ___ | 
\1 + \/ 5  + \/ 2 *\/  -5 + \/ 5  / *\1 + \/ 5  - I*\/ 2 *\/  5 - \/ 5  / 
--------------------------------------------------------------------------
                                    4
(1+5+2−5+5)2(1+5−2i5−5)24\frac{\left(1 + \sqrt{5} + \sqrt{2} \sqrt{-5 + \sqrt{5}}\right)^{2} \left(1 + \sqrt{5} - \sqrt{2} i \sqrt{5 - \sqrt{5}}\right)^{2}}{4} 
(1 + sqrt(5) + sqrt(2)*sqrt(-5 + sqrt(5)))^2*(1 + sqrt(5) - i*sqrt(2)*sqrt(5 - sqrt(5)))^2/4
Respuesta rápida [src] 
x1 = 1
x1=1x_{1} = 1 
x2 = 4
x2=4x_{2} = 4 
                             ___________
            ___       ___   /       ___ 
x3 = -1 - \/ 5  - I*\/ 2 *\/  5 - \/ 5
x3=−5−1−2i5−5x_{3} = - \sqrt{5} - 1 - \sqrt{2} i \sqrt{5 - \sqrt{5}} 
                             ___________
            ___       ___   /       ___ 
x4 = -1 - \/ 5  + I*\/ 2 *\/  5 - \/ 5
x4=−5−1+2i5−5x_{4} = - \sqrt{5} - 1 + \sqrt{2} i \sqrt{5 - \sqrt{5}} 
                          ___________
             ___         /       ___ 
       1   \/ 5         /  5   \/ 5  
x5 = - - - ----- - I*  /   - - ----- 
       4     4       \/    8     8
x5=−54−14−i58−58x_{5} = - \frac{\sqrt{5}}{4} - \frac{1}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} 
                          ___________
             ___         /       ___ 
       1   \/ 5         /  5   \/ 5  
x6 = - - - ----- + I*  /   - - ----- 
       4     4       \/    8     8
x6=−54−14+i58−58x_{6} = - \frac{\sqrt{5}}{4} - \frac{1}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} 
x6 = -sqrt(5)/4 - 1/4 + i*sqrt(5/8 - sqrt(5)/8)
Respuesta numérica [src] 
x1 = -0.809016994374947 + 0.587785252292473*i
x2 = -0.809016994374957 + 0.587785252292475*i
x3 = -0.809016994374947 + 0.587785252292473*i
x4 = 4.0
x5 = 1.0
x6 = -0.809016994374952 + 0.587785252292473*i
x7 = -0.809016994374947 + 0.587785252292474*i
x7 = -0.809016994374947 + 0.587785252292474*i
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