1952 AHSME Problems/Problem 47

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Problem

In the set of equations $z^x = y^{2x},\quad  2^z = 2\cdot4^x, \quad x + y + z = 16$, the integral roots in the order $x,y,z$ are:

$\textbf{(A) } 3,4,9 \qquad \textbf{(B) } 9,-5,-12 \qquad \textbf{(C) } 12,-5,9 \qquad \textbf{(D) } 4,3,9 \qquad \textbf{(E) } 4,9,3$

Solution #1 - Fast and Easy Solution

The easiest method, which in this case is not very time consuming, is to guess and check and use process of elimination. We can immediately rule out (B) since it does not satisfy the third equation. The first equation allows us to eliminate (A) and (C) because the bases are different. Finally, we manually check (D) and (E) and see that our answer is $\fbox{D}$


== Solution #2 $\fbox{}$

See also

1952 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 46
Followed by
Problem 48
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