Difference between revisions of "1995 AIME Problems/Problem 7"
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Revision as of 18:30, 4 July 2013
Problem
Given that and
where and are positive integers with and relatively prime, find
Solution
From the givens, , and adding to both sides gives . Completing the square on the left in the variable gives . Since , we have . Subtracting twice this from our original equation gives , so the answer is .
See also
1995 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.