Difference between revisions of "1986 AIME Problems/Problem 1"
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== Problem == | == Problem == | ||
− | What is the sum of the solutions to the equation <math>\sqrt[4]{x} = \frac{12}{7 - \sqrt[4]{x}}</math>? | + | What is the sum of the solutions to the equation <math>\displaystyle \sqrt[4]{x} = \frac{12}{7 - \sqrt[4]{x}}</math>? |
== Solution == | == Solution == |
Revision as of 19:51, 28 October 2006
Problem
What is the sum of the solutions to the equation ?
Solution
Let . Then we have
, or, by simplifying,
.
This means that
or
.
Thus the sum of the possible solutions for
is
, the answer.