2000 AIME I Problems/Problem 7
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Contents |
Problem
Suppose that 
and 
are three positive numbers that satisfy the equations 
and 
Then 
where 
and 
are relatively prime positive integers. Find 
.
Solution
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 • Resources) | ||
| Preceded by Problem 6 | Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
