Problem

Source: V International Festival of Young Mathematicians Sozopol 2014, Theme for 10-12 grade

Tags: algebra, Inequality, inequalities



Prove that for $\forall$ $x,y,z\in \mathbb{R}^+$ the following inequality is true: $\frac{x}{y+z}+\frac{25y}{z+x}+\frac{4z}{x+y}>2$.