43,3945=((0,016*9,8*1355*x)/3,6)+((0,52*1,2*1*x*x*x)/2) la ecuación
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Solución
Teorema de Cardano-Vieta
reescribamos la ecuación
$$43.3945 = \frac{x 1355 \frac{2 \cdot 49}{5 \cdot 125}}{\frac{18}{5}} + \frac{x x \frac{6 \cdot 13}{5 \cdot 25} x}{2}$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{66395 x}{351} - 139.084935897436 = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{66395}{351}$$
$$v = \frac{d}{a}$$
$$v = -139.084935897436$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = \frac{66395}{351}$$
$$x_{1} x_{2} x_{3} = -139.084935897436$$
Suma y producto de raíces
[src]
0.733194772937069 + -0.366597386468534 - 13.7681779873315*I + -0.366597386468534 + 13.7681779873315*I
$$\left(0.733194772937069 + \left(-0.366597386468534 - 13.7681779873315 i\right)\right) + \left(-0.366597386468534 + 13.7681779873315 i\right)$$
$$0$$
0.733194772937069*(-0.366597386468534 - 13.7681779873315*I)*(-0.366597386468534 + 13.7681779873315*I)
$$0.733194772937069 \left(-0.366597386468534 - 13.7681779873315 i\right) \left(-0.366597386468534 + 13.7681779873315 i\right)$$
139.084935897436 + 4.44089209850063e-16*I
$$139.084935897436 + 4.44089209850063 \cdot 10^{-16} i$$
139.084935897436 + 4.44089209850063e-16*i
$$x_{1} = 0.733194772937069$$
x2 = -0.366597386468534 - 13.7681779873315*I
$$x_{2} = -0.366597386468534 - 13.7681779873315 i$$
x3 = -0.366597386468534 + 13.7681779873315*I
$$x_{3} = -0.366597386468534 + 13.7681779873315 i$$
x3 = -0.366597386468534 + 13.7681779873315*i
x1 = -0.366597386468534 - 13.7681779873315*i
x3 = -0.366597386468534 + 13.7681779873315*i
x3 = -0.366597386468534 + 13.7681779873315*i