Sr Examen
x^3-(9/50)*x^2+0.0108*x-0.00754=0 la ecuación
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Solución
Ha introducido
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2
3 9*x
x - ---- + 0.0108*x - 0.00754 = 0
50
$$\left(0.0108 x + \left(x^{3} - \frac{9 x^{2}}{50}\right)\right) - 0.00754 = 0$$
Teorema de Cardano-Vieta
es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{9}{50}$$
$$q = \frac{c}{a}$$
$$q = 0.0108$$
$$v = \frac{d}{a}$$
$$v = -0.00754$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = \frac{9}{50}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0.0108$$
$$x_{1} x_{2} x_{3} = -0.00754$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{9}{50}$$
$$q = \frac{c}{a}$$
$$q = 0.0108$$
$$v = \frac{d}{a}$$
$$v = -0.00754$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = \frac{9}{50}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0.0108$$
$$x_{1} x_{2} x_{3} = -0.00754$$
Respuesta rápida
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x1 = 0.254200098213753
$$x_{1} = 0.254200098213753$$
x2 = -0.0371000491068765 - 0.168182218470543*I
$$x_{2} = -0.0371000491068765 - 0.168182218470543 i$$
x3 = -0.0371000491068765 + 0.168182218470543*I
$$x_{3} = -0.0371000491068765 + 0.168182218470543 i$$
x3 = -0.0371000491068765 + 0.168182218470543*i
Suma y producto de raíces
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suma
0.254200098213753 + -0.0371000491068765 - 0.168182218470543*I + -0.0371000491068765 + 0.168182218470543*I
$$\left(0.254200098213753 + \left(-0.0371000491068765 - 0.168182218470543 i\right)\right) + \left(-0.0371000491068765 + 0.168182218470543 i\right)$$
=
0.180000000000000
$$0.18$$
producto
0.254200098213753*(-0.0371000491068765 - 0.168182218470543*I)*(-0.0371000491068765 + 0.168182218470543*I)
$$0.254200098213753 \left(-0.0371000491068765 - 0.168182218470543 i\right) \left(-0.0371000491068765 + 0.168182218470543 i\right)$$
=
0.00754 + 4.33680868994202e-19*I
$$0.00754 + 4.33680868994202 \cdot 10^{-19} i$$
0.00754 + 4.33680868994202e-19*i
Respuesta numérica
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x1 = -0.0371000491068765 + 0.168182218470543*i
x2 = 0.254200098213753
x3 = -0.0371000491068765 - 0.168182218470543*i
x3 = -0.0371000491068765 - 0.168182218470543*i