Solve the quadratic equation for $x : 4 x^{2} - 4 a^{2} x (a^{4} - b^{4}) = 0$ .

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Solution

Given: $4 x^{2} - 4 a^{2} x (a^{4} - b^{4}) = 0$
$4 x [x - a^{2} (a^{4} - b^{4})] = 0$
$\Rightarrow 4 x = 0$ or $x - a^{2} (a^{4} - b^{4}) = 0$
$∴ x = 0, x = a^{2} (a^{4} - b^{4})$

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