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1954 AHSME Problems/Problem 1

Revision as of 13:33, 6 June 2016 by Katzrockso (talk | contribs) (Created page with "== Problem 1== The square of <math>5-\sqrt{y^2-25}</math> is: <math>\textbf{(A)}\ y^2-5\sqrt{y^2-25} \qquad \textbf{(B)}\ -y^2 \qquad \textbf{(C)}\ y^2 \\ \textbf{(D)}\ (5-...")
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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

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

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