1958 AHSME Problems/Problem 11

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Problem

The number of roots satisfying the equation $\sqrt{5 - x} = x\sqrt{5 - x}$ is:

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

Solution

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 $\to \boxed{\textbf{(C)}}$


See also

1958 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions

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