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.
Let ,
,
be positive real numbers. Prove that
Since all terms are homogeneous, we may assume WLOG that .
Then the LHS becomes .
Notice , so
.
So , as desired.
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