Problem

Source: 2016 JBMO TST- Macedonia

Tags: JMMO, Macedonia, Junior, 2016, algebra, Inequality



Let $x$, $y$, and $z$ be positive real numbers. Prove that $\sqrt {\frac {xy}{x^2 + y^2 + 2z^2}} + \sqrt {\frac {yz}{y^2 + z^2 + 2x^2}}+\sqrt {\frac {zx}{z^2 + x^2 + 2y^2}} \le \frac{3}{2}$. When does equality hold?