2011 JBMO Problems/Problem 1
Revision as of 19:24, 8 September 2018 by Rockmanex3 (talk | contribs)
Problem
Let be positive real numbers such that
. Prove that:
Solution
Since ,
. By AM-GM Inequality,
Adding the inequalities together and factoring yields
Since
are positive,
,
, and
are all greater than 0. That means
See Also
2011 JBMO (Problems • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 | ||
All JBMO Problems and Solutions |