2012 IMO Problems/Problem 2
Problem
Let be positive real numbers that satisfy . Prove that
Solution
The inequality between arithmetic and geometric mean implies The inequality is strict unless . Multiplying analogous inequalities for yields
See Also
2012 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |