IMO Shortlist 2001 problem A6

Prove that for all positive real numbers $a,b,c$ , $\frac{a}{\sqrt{a^2 + 8bc}} + \frac{b}{\sqrt{b^2 + 8ca}} + \frac{c}{\sqrt{c^2 + 8ab}} \geq 1.$

Source: Međunarodna matematička olimpijada, shortlist 2001

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