2001 IMO Problems/Problem 2
Problem
Let be positive real numbers. Prove that
Solution
Solution using Holder's
By Holder's inequality, Thus we need only show that Which is obviously true since .
Alternate Solution using Jensen's
By Jensen's, , so we need to prove , which is obvious by RMS-AM-GM-HM.
2001 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
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