$4 x^{3} - 4 x + 4 y = 0$ and $4 y^{3} + 4 x - 4 y = 0$ , find $x$ and $y$

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Solution

$4 x^{3} - 4 x + 4 y = 0$
$4 x^{3} = 4 x - 4 y$
And $4 y^{3} - 4 x + 4 y = 0$
So, $4 y^{3} + 4 x^{3} = 0$
$⟹ y^{3} + x^{3} = 0$
$⟹ y = - x$
So, $4 x^{3} - 4 x + 4 y = 0$
$⟹ 4 x^{3} - 4 x + 4 x = 0$
$⟹ x (x^{2} - 2) = 0$
So, $x = 0 x = \pm \sqrt{2}$

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