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2*x^3-6*x+5=0

2*x^3-6*x+5=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   3              
2*x  - 6*x + 5 = 0
(2x3−6x)+5=0\left(2 x^{3} - 6 x\right) + 5 = 0
Simplificar
Teorema de Cardano-Vieta
reescribamos la ecuación
(2x3−6x)+5=0\left(2 x^{3} - 6 x\right) + 5 = 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
x3−3x+52=0x^{3} - 3 x + \frac{5}{2} = 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=−3q = -3
v=dav = \frac{d}{a}
v=52v = \frac{5}{2}
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=−3x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -3
x1x2x3=52x_{1} x_{2} x_{3} = \frac{5}{2}
Gráfica
-17.5-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.510.0-50005000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
                2/3
       3 ___   2   
x1 = - \/ 2  - ----
                2
x1=−23−2232x_{1} = - \sqrt[3]{2} - \frac{2^{\frac{2}{3}}}{2} 
     3 ___    2/3     /  3 ___   ___    2/3   ___\
     \/ 2    2        |  \/ 2 *\/ 3    2   *\/ 3 |
x2 = ----- + ---- + I*|- ----------- + ----------|
       2      4       \       2            4     /
x2=2234+232+i(−2332+22334)x_{2} = \frac{2^{\frac{2}{3}}}{4} + \frac{\sqrt[3]{2}}{2} + i \left(- \frac{\sqrt[3]{2} \sqrt{3}}{2} + \frac{2^{\frac{2}{3}} \sqrt{3}}{4}\right) 
     3 ___    2/3     /3 ___   ___    2/3   ___\
     \/ 2    2        |\/ 2 *\/ 3    2   *\/ 3 |
x3 = ----- + ---- + I*|----------- - ----------|
       2      4       \     2            4     /
x3=2234+232+i(−22334+2332)x_{3} = \frac{2^{\frac{2}{3}}}{4} + \frac{\sqrt[3]{2}}{2} + i \left(- \frac{2^{\frac{2}{3}} \sqrt{3}}{4} + \frac{\sqrt[3]{2} \sqrt{3}}{2}\right) 
x3 = 2^(2/3)/4 + 2^(1/3)/2 + i*(-2^(2/3)*sqrt(3)/4 + 2^(1/3)*sqrt(3)/2)
Suma y producto de raíces [src] 
suma
           2/3   3 ___    2/3     /  3 ___   ___    2/3   ___\   3 ___    2/3     /3 ___   ___    2/3   ___\
  3 ___   2      \/ 2    2        |  \/ 2 *\/ 3    2   *\/ 3 |   \/ 2    2        |\/ 2 *\/ 3    2   *\/ 3 |
- \/ 2  - ---- + ----- + ---- + I*|- ----------- + ----------| + ----- + ---- + I*|----------- - ----------|
           2       2      4       \       2            4     /     2      4       \     2            4     /
((−23−2232)+(2234+232+i(−2332+22334)))+(2234+232+i(−22334+2332))\left(\left(- \sqrt[3]{2} - \frac{2^{\frac{2}{3}}}{2}\right) + \left(\frac{2^{\frac{2}{3}}}{4} + \frac{\sqrt[3]{2}}{2} + i \left(- \frac{\sqrt[3]{2} \sqrt{3}}{2} + \frac{2^{\frac{2}{3}} \sqrt{3}}{4}\right)\right)\right) + \left(\frac{2^{\frac{2}{3}}}{4} + \frac{\sqrt[3]{2}}{2} + i \left(- \frac{2^{\frac{2}{3}} \sqrt{3}}{4} + \frac{\sqrt[3]{2} \sqrt{3}}{2}\right)\right) 
=
  /3 ___   ___    2/3   ___\     /  3 ___   ___    2/3   ___\
  |\/ 2 *\/ 3    2   *\/ 3 |     |  \/ 2 *\/ 3    2   *\/ 3 |
I*|----------- - ----------| + I*|- ----------- + ----------|
  \     2            4     /     \       2            4     /
i(−2332+22334)+i(−22334+2332)i \left(- \frac{\sqrt[3]{2} \sqrt{3}}{2} + \frac{2^{\frac{2}{3}} \sqrt{3}}{4}\right) + i \left(- \frac{2^{\frac{2}{3}} \sqrt{3}}{4} + \frac{\sqrt[3]{2} \sqrt{3}}{2}\right) 
producto
/           2/3\ /3 ___    2/3     /  3 ___   ___    2/3   ___\\ /3 ___    2/3     /3 ___   ___    2/3   ___\\
|  3 ___   2   | |\/ 2    2        |  \/ 2 *\/ 3    2   *\/ 3 || |\/ 2    2        |\/ 2 *\/ 3    2   *\/ 3 ||
|- \/ 2  - ----|*|----- + ---- + I*|- ----------- + ----------||*|----- + ---- + I*|----------- - ----------||
\           2  / \  2      4       \       2            4     // \  2      4       \     2            4     //
(−23−2232)(2234+232+i(−2332+22334))(2234+232+i(−22334+2332))\left(- \sqrt[3]{2} - \frac{2^{\frac{2}{3}}}{2}\right) \left(\frac{2^{\frac{2}{3}}}{4} + \frac{\sqrt[3]{2}}{2} + i \left(- \frac{\sqrt[3]{2} \sqrt{3}}{2} + \frac{2^{\frac{2}{3}} \sqrt{3}}{4}\right)\right) \left(\frac{2^{\frac{2}{3}}}{4} + \frac{\sqrt[3]{2}}{2} + i \left(- \frac{2^{\frac{2}{3}} \sqrt{3}}{4} + \frac{\sqrt[3]{2} \sqrt{3}}{2}\right)\right) 
=
-5/2
−52- \frac{5}{2} 
-5/2
Respuesta numérica [src] 
x1 = 1.02681078793949 - 0.40375881747242*i
x2 = 1.02681078793949 + 0.40375881747242*i
x3 = -2.05362157587897
x3 = -2.05362157587897
Gráfico
2*x^3-6*x+5=0 la ecuación
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