Solve the following quadratic equation: 4x^2 - 4a^2x + (a^4 - b^4… - Vidyadip

Question

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

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Answer

$4x^2 - 4a^2x + (a^4 - b^4) = 0$
$\Rightarrow 4x^2 - 2(a^2 + b^2)x - 2(a^2 - b^2)x + (a^4 - b^4) = 0$
$\Rightarrow 2x[2x - (a^2 + b^2)] - (a^2 - b^2)[2x + (a^2+ b^2)] = 0$
$\Rightarrow [2x - (a^2 + b^2)][2x - (a^2 - b^2)] = 0$
$\Rightarrow 2x - (a^2 + b^2) = 0$ or $2x - (a^2 - b^2) = 0$
$\Rightarrow\text{x}=\frac{\text{a}^2+\text{b}^2}{2}$ or $\text{x}=\frac{\text{a}^2-\text{b}^2}{2}$

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