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IMO LongList 1967, Poland 3

Source: IMO LongList 1967, Poland 3

December 16, 2004
Inequalitythree variable inequalityMuirheadIMO ShortlistIMO Longlistalgebrainequalities proposed

Problem Statement

Prove that for arbitrary positive numbers the following inequality holds 1a+1b+1c≤a8+b8+c8a3b3c3.\frac{1}{a} + \frac{1}{b} + \frac{1}{c} \leq \frac{a^8 + b^8 + c^8}{a^3b^3c^3}.
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