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> | + | What is the sum of the solutions to the equation <math>\sqrt[4]{x} = \frac{12}{7 - \sqrt[4]{x}}</math>? |
== Solution == | == Solution == | ||
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* [[American Invitational Mathematics Examination]] | * [[American Invitational Mathematics Examination]] | ||
* [[Mathematics competition resources]] | * [[Mathematics competition resources]] | ||
+ | {{MAA Notice}} |
Revision as of 19:04, 4 July 2013
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
.
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 |
- AIME Problems and Solutions
- American Invitational Mathematics Examination
- Mathematics competition resources
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.