2012 USAJMO Problems/Problem 3
Problem
Let ,
,
be positive real numbers. Prove that
Solution
By the Cauchy-Schwarz inequality,
so
Since
,
Hence,
Again by the Cauchy-Schwarz inequality,
so
Since
,
Hence,
Therefore,
See Also
2012 USAJMO (Problems • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAJMO Problems and Solutions |