1954 AHSME Problems/Problem 1

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Problem 1

The square of $5-\sqrt{y^2-25}$ is:

$\textbf{(A)}\ y^2-5\sqrt{y^2-25} \qquad \textbf{(B)}\ -y^2 \qquad \textbf{(C)}\ y^2 \\ \textbf{(D)}\ (5-y)^2\qquad\textbf{(E)}\ y^2-10\sqrt{y^2-25}$

Solution

$(5-\sqrt{y^2-25})^2 = 5^2-2\cdot 5\cdot\sqrt{y^2-25}+y^2-25 = y^2-10\sqrt{y^2-25}$ $\ \Rightarrow$ $\fbox{E}$

See Also

1954 AHSC (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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