1986 AIME Problems/Problem 1
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Problem
What is the sum of the solutions to the equation ![\displaystyle \sqrt[4]{x} = \frac{12}{7 - \sqrt[4]{x}}](http://data.artofproblemsolving.com/images/latex/f/2/0/f2081d064c4db8fe12410994351be29402c7a9da.gif "\displaystyle \sqrt[4]{x} = \frac{12}{7 - \sqrt[4]{x}}")
?
Solution
Let ![y = \sqrt[4]{x}](http://data.artofproblemsolving.com/images/latex/5/6/b/56be7cb4d488cb06969743a2bb0a32832918a878.gif "y = \sqrt[4]{x}")
. Then we have
, or, by simplifying,
This means that ![\sqrt[4]{x} = y = 3](http://data.artofproblemsolving.com/images/latex/f/8/a/f8afdf23339911e0318bb691be5eb710ac3d8563.gif "\sqrt[4]{x} = y = 3")
or 
.
Thus the sum of the possible solutions for 
is 
.
See also
| 1986 AIME (Problems • Resources) | ||
| Preceded by First Question | Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
