Sr Examen
4x^3(-(y^2-1)^3+1)=0 la ecuación
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Solución
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/ 3 \ 3 | / 2 \ | 4*x *\- \y - 1/ + 1/ = 0
$$4 x^{3} \left(1 - \left(y^{2} - 1\right)^{3}\right) = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$4 x^{3} \left(1 - \left(y^{2} - 1\right)^{3}\right) = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$\frac{4 x^{3} \left(1 - \left(y^{2} - 1\right)^{3}\right)}{4 - 4 \left(y^{2} - 1\right)^{3}} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = 0$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = 0$$
$$4 x^{3} \left(1 - \left(y^{2} - 1\right)^{3}\right) = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$\frac{4 x^{3} \left(1 - \left(y^{2} - 1\right)^{3}\right)}{4 - 4 \left(y^{2} - 1\right)^{3}} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = 0$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = 0$$
Gráfica