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smc

algebra intermediate

Problem

A value of

x

satisfying the equation

x^{2} + b^{2} = (a - x)^{2}

is:

(A)

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

(B)

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

(C)

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

(D)

\frac{a - b}{2}

Solution

Solve for x:

x^{2} + b^{2} = (a - x)^{2}

x^{2} + b^{2} = x^{2} - 2 a x + a^{2}

b^{2} = - 2 a x + a^{2}

2 a x = a^{2} - b^{2}

x = \frac{a ^{2} - b ^{2}}{2 a} \to \frac{a ^{2} - b ^{2}}{2 a}

Final answer

C