IMO Shortlist 2001 problem A6


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2. travnja 2012.
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Prove that for all positive real numbers a,b,c, \frac{a}{\sqrt{a^2 + 8bc}} + \frac{b}{\sqrt{b^2 + 8ca}} + \frac{c}{\sqrt{c^2 + 8ab}} \geq 1.
Izvor: Međunarodna matematička olimpijada, shortlist 2001