Sr Examen

Otras calculadoras

x^3+3*x-2=0

x^3+3*x-2=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

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=3q = 3
v=dav = \frac{d}{a}
v=−2v = -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=−2x_{1} x_{2} x_{3} = -2
Gráfica
-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.515.0-25002500
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
                           ___________     /                              ___________\
                        3 /       ___      |         ___           ___ 3 /       ___ |
            1           \/  1 + \/ 2       |       \/ 3          \/ 3 *\/  1 + \/ 2  |
x1 = ---------------- - -------------- + I*|- ---------------- - --------------------|
          ___________         2            |       ___________            2          |
       3 /       ___                       |    3 /       ___                        |
     2*\/  1 + \/ 2                        \  2*\/  1 + \/ 2                         /
x1=−1+232+121+23+i(−31+232−321+23)x_{1} = - \frac{\sqrt[3]{1 + \sqrt{2}}}{2} + \frac{1}{2 \sqrt[3]{1 + \sqrt{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{1 + \sqrt{2}}}{2} - \frac{\sqrt{3}}{2 \sqrt[3]{1 + \sqrt{2}}}\right) 
                           ___________     /                            ___________\
                        3 /       ___      |       ___           ___ 3 /       ___ |
            1           \/  1 + \/ 2       |     \/ 3          \/ 3 *\/  1 + \/ 2  |
x2 = ---------------- - -------------- + I*|---------------- + --------------------|
          ___________         2            |     ___________            2          |
       3 /       ___                       |  3 /       ___                        |
     2*\/  1 + \/ 2                        \2*\/  1 + \/ 2                         /
x2=−1+232+121+23+i(321+23+31+232)x_{2} = - \frac{\sqrt[3]{1 + \sqrt{2}}}{2} + \frac{1}{2 \sqrt[3]{1 + \sqrt{2}}} + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{1 + \sqrt{2}}} + \frac{\sqrt{3} \sqrt[3]{1 + \sqrt{2}}}{2}\right) 
        ___________                 
     3 /       ___          1       
x3 = \/  1 + \/ 2   - --------------
                         ___________
                      3 /       ___ 
                      \/  1 + \/ 2
x3=−11+23+1+23x_{3} = - \frac{1}{\sqrt[3]{1 + \sqrt{2}}} + \sqrt[3]{1 + \sqrt{2}} 
x3 = -1/(1 + sqrt(2))^(1/3) + (1 + sqrt(2))^(1/3)
Suma y producto de raíces [src] 
suma
                      ___________     /                              ___________\                         ___________     /                            ___________\                                  
                   3 /       ___      |         ___           ___ 3 /       ___ |                      3 /       ___      |       ___           ___ 3 /       ___ |      ___________                 
       1           \/  1 + \/ 2       |       \/ 3          \/ 3 *\/  1 + \/ 2  |          1           \/  1 + \/ 2       |     \/ 3          \/ 3 *\/  1 + \/ 2  |   3 /       ___          1       
---------------- - -------------- + I*|- ---------------- - --------------------| + ---------------- - -------------- + I*|---------------- + --------------------| + \/  1 + \/ 2   - --------------
     ___________         2            |       ___________            2          |        ___________         2            |     ___________            2          |                       ___________
  3 /       ___                       |    3 /       ___                        |     3 /       ___                       |  3 /       ___                        |                    3 /       ___ 
2*\/  1 + \/ 2                        \  2*\/  1 + \/ 2                         /   2*\/  1 + \/ 2                        \2*\/  1 + \/ 2                         /                    \/  1 + \/ 2
(−11+23+1+23)+((−1+232+121+23+i(−31+232−321+23))+(−1+232+121+23+i(321+23+31+232)))\left(- \frac{1}{\sqrt[3]{1 + \sqrt{2}}} + \sqrt[3]{1 + \sqrt{2}}\right) + \left(\left(- \frac{\sqrt[3]{1 + \sqrt{2}}}{2} + \frac{1}{2 \sqrt[3]{1 + \sqrt{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{1 + \sqrt{2}}}{2} - \frac{\sqrt{3}}{2 \sqrt[3]{1 + \sqrt{2}}}\right)\right) + \left(- \frac{\sqrt[3]{1 + \sqrt{2}}}{2} + \frac{1}{2 \sqrt[3]{1 + \sqrt{2}}} + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{1 + \sqrt{2}}} + \frac{\sqrt{3} \sqrt[3]{1 + \sqrt{2}}}{2}\right)\right)\right) 
=
  /                            ___________\     /                              ___________\
  |       ___           ___ 3 /       ___ |     |         ___           ___ 3 /       ___ |
  |     \/ 3          \/ 3 *\/  1 + \/ 2  |     |       \/ 3          \/ 3 *\/  1 + \/ 2  |
I*|---------------- + --------------------| + I*|- ---------------- - --------------------|
  |     ___________            2          |     |       ___________            2          |
  |  3 /       ___                        |     |    3 /       ___                        |
  \2*\/  1 + \/ 2                         /     \  2*\/  1 + \/ 2                         /
i(−31+232−321+23)+i(321+23+31+232)i \left(- \frac{\sqrt{3} \sqrt[3]{1 + \sqrt{2}}}{2} - \frac{\sqrt{3}}{2 \sqrt[3]{1 + \sqrt{2}}}\right) + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{1 + \sqrt{2}}} + \frac{\sqrt{3} \sqrt[3]{1 + \sqrt{2}}}{2}\right) 
producto
/                      ___________     /                              ___________\\ /                      ___________     /                            ___________\\                                  
|                   3 /       ___      |         ___           ___ 3 /       ___ || |                   3 /       ___      |       ___           ___ 3 /       ___ || /   ___________                 \
|       1           \/  1 + \/ 2       |       \/ 3          \/ 3 *\/  1 + \/ 2  || |       1           \/  1 + \/ 2       |     \/ 3          \/ 3 *\/  1 + \/ 2  || |3 /       ___          1       |
|---------------- - -------------- + I*|- ---------------- - --------------------||*|---------------- - -------------- + I*|---------------- + --------------------||*|\/  1 + \/ 2   - --------------|
|     ___________         2            |       ___________            2          || |     ___________         2            |     ___________            2          || |                    ___________|
|  3 /       ___                       |    3 /       ___                        || |  3 /       ___                       |  3 /       ___                        || |                 3 /       ___ |
\2*\/  1 + \/ 2                        \  2*\/  1 + \/ 2                         // \2*\/  1 + \/ 2                        \2*\/  1 + \/ 2                         // \                 \/  1 + \/ 2  /
(−1+232+121+23+i(321+23+31+232))(−1+232+121+23+i(−31+232−321+23))(−11+23+1+23)\left(- \frac{\sqrt[3]{1 + \sqrt{2}}}{2} + \frac{1}{2 \sqrt[3]{1 + \sqrt{2}}} + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{1 + \sqrt{2}}} + \frac{\sqrt{3} \sqrt[3]{1 + \sqrt{2}}}{2}\right)\right) \left(- \frac{\sqrt[3]{1 + \sqrt{2}}}{2} + \frac{1}{2 \sqrt[3]{1 + \sqrt{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{1 + \sqrt{2}}}{2} - \frac{\sqrt{3}}{2 \sqrt[3]{1 + \sqrt{2}}}\right)\right) \left(- \frac{1}{\sqrt[3]{1 + \sqrt{2}}} + \sqrt[3]{1 + \sqrt{2}}\right) 
=
2
22 
2
Respuesta numérica [src] 
x1 = -0.298035818991661 + 1.80733949445202*i
x2 = -0.298035818991661 - 1.80733949445202*i
x3 = 0.596071637983322
x3 = 0.596071637983322
Gráfico
x^3+3*x-2=0 la ecuación
    © Sr Examen – Калькулятор