Junior Balkan MO 2016 - Problem 2
Let be positive real numbers.Prove that
Let $a,b,c$ be positive real numbers.Prove that
\[\frac{8}{(a+b)^2 + 4abc} + \frac{8}{(b+c)^2 + 4abc} + \frac{8}{(a+c)^2 + 4abc} + a^2 + b^2 + c ^2 \ge \frac{8}{a+3} + \frac{8}{b+3} + \frac{8}{c+3} \text.\]
Source: Juniorska balkanska matematička olimpijada 2016.