1958 AHSME Problems/Problem 9

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Problem

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

$\textbf{(A)}\ \frac{b^2 + a^2}{2a}\qquad  \textbf{(B)}\ \frac{b^2 - a^2}{2a}\qquad  \textbf{(C)}\ \frac{a^2 - b^2}{2a}\qquad  \textbf{(D)}\ \frac{a - b}{2}\qquad  \textbf{(E)}\ \frac{a^2 - b^2}{2}$

Solution

Solve for x:

\[x^2+b^2=(a-x)^2\] \[x^2+b^2=x^2-2ax+a^2\] \[b^2=-2ax+a^2\] \[2ax=a^2-b^2\] \[x=\frac{a^2-b^2}{2a} \to \boxed{\text{(C)}}\]


See Also

1958 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
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