The value of $x$ satisfying the equation $x^{2} + p^{2} = (q - x)^{2}$ is

\frac{p^{2} - q^{2}}{2}

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\frac{q^{2} - p^{2}}{2 q}

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\frac{q^{2} - p^{2}}{2}

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\frac{p^{2} - q^{2}}{2 q}

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Solution

The correct option is B $\frac{q^{2} - p^{2}}{2 q}$
Given Equation:
$x^{2} + p^{2} = {(q - x)}^{2}$
$\Rightarrow x^{2} + p^{2} = q^{2} - 2 q x + x^{2}$
$\Rightarrow x^{2} + 2 q x - x^{2} = q^{2} - p^{2}$
$\Rightarrow 2 q x = q^{2} - p^{2}$
$\Rightarrow x = \frac{q^{2} - p^{2}}{2 q}$

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