1952 AHSME Problems/Problem 47

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 $\fbox{}$

1952 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 46	Followed by Problem 48
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1952 AHSME Problems/Problem 47

Problem

Solution #1 - Fast and Easy Solution

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