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

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Solution

$4 x^{2} - 4 a^{2} x + (a^{4} - b^{4}) = 0$
$⟹ 4 x^{2} - 4 a^{2} x + a^{4} = b^{4}$
$⟹ (2 x - a^{2})^{2} = b^{4}$
$⟹ 2 x - a^{2} = \pm b^{2}$
$⟹ 2 x = a^{2} \pm b^{2}$
$⟹ R o o t s o f g i v e n q u a d r a t i c e q u a t i o n a r e :$

$x_{1} = \frac{a^{2} + b^{2}}{2}, x_{2} = \frac{a^{2} - b^{2}}{2}$

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