Difference between revisions of "1986 AIME Problems/Problem 1"
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== See also == | == See also == | ||
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{{AIME box|year=1986|before=First Question|num-a=2}} | {{AIME box|year=1986|before=First Question|num-a=2}} | ||
| + | * [[AIME Problems and Solutions]] | ||
| + | * [[American Invitational Mathematics Examination]] | ||
| + | * [[Mathematics competition resources]] | ||
Revision as of 13:37, 6 May 2007
Problem
What is the sum of the solutions to the equation ![$\displaystyle \sqrt[4]{x} = \frac{12}{7 - \sqrt[4]{x}}$](http://latex.artofproblemsolving.com/f/d/7/fd73a04a5a41ae82d5b13c2822f5adeaeb128820.png)
?
Solution
Let ![$y = \sqrt[4]{x}$](http://latex.artofproblemsolving.com/f/5/8/f5838ae6bb955f1f7afe1c28d870b6cd091b78ac.png)
. Then we have
, or, by simplifying,
.
This means that ![$\sqrt[4]{x} = y = 3$](http://latex.artofproblemsolving.com/7/2/3/723fc9924d37616a4675a26e831751451b6904d6.png)
or 
.
Thus the sum of the possible solutions for 
is 
, the answer.
See also
| 1986 AIME (Problems • Answer Key • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
