Question

SOLVE BY CARDAN'S METHOD
x^3 +12x-12=0​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

$\sf f(x) = {x}^{3} + 12x - 12 = 0$

Using the cubic formula by Gerolemo Cardano.

$\sf x _{ 1,2,3 } = \omega_{k} \sqrt[3]{6 + 10 } + \omega _{k}^{2} \sqrt[3]{6 - 10}$

$\sf x_{1,2,3} = 2\omega_{k}\sqrt[3]{2} - \omega_{k}^{2} \sqrt[3]{4}$

Therefore, All three solutions are:

$\bf x_1 = 2 \sqrt[3]{2} - \sqrt[3]{4}$

$\bf x_{2,3} = ( \frac{ \sqrt[3]{4} }{2} - \sqrt[3]{2} ) \pm i( \sqrt[6]{108} + \frac{\sqrt[6]{432} }{2})$