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1976 AHSME Problems/Problem 2

Revision as of 18:52, 12 July 2020 by Mathjams (talk | contribs) (Created page with "== Problem 2 == For how many real numbers <math>x</math> is <math>\sqrt{-(x+1)^2}</math> a real number? <math>\textbf{(A) }\text{none}\qquad \textbf{(B) }\text{one}\qquad \te...")
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Problem 2

For how many real numbers $x$ is $\sqrt{-(x+1)^2}$ a real number?

$\textbf{(A) }\text{none}\qquad \textbf{(B) }\text{one}\qquad \textbf{(C) }\text{two}\qquad\\ \textbf{(D) }\text{a finite number greater than two}\qquad \textbf{(E) }\infty$

Solution

$\sqrt{-(x+1)^2}$ is a real number, if and only if $-(x+1)^2$ is nonnegative. Since $(x+1)^2$ is always nonnegative, $-(x+1)^2$ is nonnegative only when $-(x+1)^2=0$, or when $x=-1 \Rightarrow \textbf{(B)}$.
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