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42nd International Mathematical Olympiad


IMO 2001 Problems and Solutions

Washinton, DC, USA
July 1-14, 2001



Problem 2

for all positive real numbers a, b and c.




Solution

First we shall prove that

or equivalently, that

The AM-GM inequality yields

Thus

so

Similarly, we have

Adding these three inequalities yields

Comment. The proposer conjectures that for any a, b, c > 0 and >= 8, the following inequality holds: