Difference between revisions of "1976 AHSME Problems/Problem 2"

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 $x=-1 \Rightarrow \textbf{(B)}$.

1976 AHSME Problems

 1976 AHSME (Problems • Answer Key • Resources) Preceded by1975 AHSME Followed by1977 AHSME 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 All AHSME Problems and Solutions