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

Question

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

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Answer

$4x^2 + 4bx - (a^2 - b^2) = 0$
$\Rightarrow 4x^2 + 4bx + (b^2 - a^2) = 0$
$\Rightarrow 4x^2 + 2(b + a)x + 2(b - a)x + (b^2 - a^2) = 0$
$\Rightarrow 2x[2x + (b + a)] + (b - a)[2x + (b + a)] = 0$
$\Rightarrow [2x + (b + a)][2x + (b - a)] = 0$
$\Rightarrow 2x + (b - a) = 0 or 2x + 9b - a = 0$
$\Rightarrow\text{x}=\frac{-(\text{b}+\text{a})}{2}$ or $\text{x}=\frac{-(\text{b}-\text{a})}{2}$
$\Rightarrow\text{x}=\frac{-(\text{a}+\text{b})}{2}$ or $\text{x}=\frac{(\text{a}-\text{b})}{2}$

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