1959 AHSME Problems/Problem 38
Problem
If 
, then 
:
Solution
Subtract 
from both sides of the initial equation and solve for :
\begin{align*}
\sqrt{2x} &= 1-4x \\
2x &= 1-8x+16x^2 \\
16x^2-10x+1 &= 0 \\
(8x-1)(2x-1) &= 0
\end{align*}
It may look like we have two different solutions for , but plugging in 
into the original equation reveals that it is extraneous. Thus, 
, which is only consistent with answer choice 
.
See also
| 1959 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 37 |
Followed by Problem 39 | |
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The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
