Find the value of $x$ :
$x^{2} + p^{2} = (q - x)^{2}$

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

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

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

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

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Solution

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

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