Difference between revisions of "1952 AHSME Problems/Problem 47"

Revision as of 17:43, 2 October 2014

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:

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

$\fbox{}$

1952 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 46	Followed by Problem 48
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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 == Problem ==
-In the set of equations <math>z^x = y^{2x},\quad  2^z = 2\cdot4^x, \quadx + y + z = 16</math>, the integral roots in the order <math>x,y,z</math> are:
+In the set of equations <math>z^x = y^{2x},\quad  2^z = 2\cdot4^x, \quad x + y + z = 16</math>, the integral roots in the order <math>x,y,z</math> are:
 <math>\textbf{(A) } 3,4,9 \qquad