2003 USAMO Problems/Problem 5
Problem
Let , , be positive real numbers. Prove that
Solution
Since all terms are homogeneous, we may assume WLOG that .
Then the LHS becomes .
Notice , so .
So , as desired.
See also
2003 USAMO (Problems • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |