2016 JBMO Problems/Problem 2

Problem

Let $a,b,c$ be positive real numbers. Prove that

$\frac{8}{(a+b)^2 + 4abc} + \frac{8}{(b+c)^2 + 4abc} + \frac{8}{(a+c)^2 + 4abc} + a^2 + b^2 + c ^2 \ge \frac{8}{a+3} + \frac{8}{b+3} + \frac{8}{c+3}$ .

2016 JBMO (Problems • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4
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2016 JBMO Problems/Problem 2

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