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

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Solution

Given,
$4 x^{2} - 2 (a^{2} + b^{2}) x + a^{2} b^{2} = 0$
For general Quadratic Equation,
$a x^{2} + b x + c = 0$
$a = 4, b = - 2 (a^{2} + b^{2}), c = a^{2} b^{2}$
According to formulae,
$x = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a} = \frac{a^{2}}{2}$
$x = \frac{- b - \sqrt{b^{2} - 4 a c}}{2 a} = \frac{b^{2}}{2}$

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