1958 AHSME Problems/Problem 11

Problem

The number of roots satisfying the equation $\sqrt{5 \minus{} x} \equal{} x\sqrt{5 \minus{} x}$ (Error compiling LaTeX. Unknown error_msg) is:

$\textbf{(A)}\ \text{unlimited}\qquad \textbf{(B)}\ 3\qquad \textbf{(C)}\ 2\qquad \textbf{(D)}\ 1\qquad \textbf{(E)}\ 0$

Solve the equation for x.

$\sqrt{5-x}=x\sqrt{5-x}$

$x\sqrt{5-x} - \sqrt{5-x} = 0$

$(x-1)\sqrt{5-x}=0$

$x=1,5$

There are two solutions $\to \boxed{\textbf{(C)}}$

1958 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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