2009 USAMO Problems/Problem 4
Revision as of 12:44, 4 July 2013 by Nathan wailes (talk | contribs)
Problem
For let , , ..., be positive real numbers such that
Prove that max .
Solution
Assume without loss of generality that . Now we seek to prove that .
By the Cauchy-Schwarz Inequality, Since , clearly , dividing yields:
as desired.
See Also
2009 USAMO (Problems • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.