Problem

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2020 p3

Tags: algebra, inequalities



Let $x, y, z \in R^+$. Prove that $$\frac{x}{x +\sqrt{(x + y)(x + z)}}+\frac{y}{y +\sqrt{(y + z)(y + x)}}+\frac{z}{z +\sqrt{(x + z)(z + y)}} \le 1$$