2000 IMO Problems/Problem 2
Problem
Let be positive real numbers with . Show that
Solution
There exist positive reals , , such that , , . The inequality then rewrites as or Set ,,, we get Since at most one of can be negative (if 2 or more are negative, then one of will become negative), for all positive we apply AM-GM, for one negative we have .
See Also
2000 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |