A value of x satisfying the equation $x^{2} + b^{2} = (a - x)^{2}$ is:

\frac{b^{2} + a^{2}}{2 a}

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\frac{b^{2} - a^{2}}{2 a}

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\frac{a^{2} - b^{2}}{2 a}

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\frac{a - b}{2}

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Solution

The correct option is C $\frac{a^{2} - b^{2}}{2 a}$
$x^{2} + b^{2} = {(a - x)}^{2} ⟹ x^{2} + b^{2} = a^{2} - 2 a x + x^{2} ⟹ 2 a x = a^{2} - b^{2} ∴ x = \frac{a^{2} - b^{2}}{2 a}$

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