2000 AIME I Problems/Problem 7
Contents
[hide]Problem
Suppose that and are three positive numbers that satisfy the equations and Then where and are relatively prime positive integers. Find .
Solution 1
Let .
Thus . So .
Solution 2
Since , so . Also, by the second equation. Substitution gives , , and , so the solution is .
See also
2000 AIME I (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 |
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