IMO Shortlist 1967 problem 3
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arhiva2. travnja 2012. Prove that for arbitrary positive numbers the following inequality holds
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Prove that for arbitrary positive numbers the following inequality holds
$$\frac{1}{a} + \frac{1}{b} + \frac{1}{c} \leq \frac{a^8 + b^8 + c^8}{a^3b^3c^3}.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1967
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