May 20, 2019 Thread starter #1 Olinguito Well-known member Apr 22, 2018 251 Let $x,y,z$ be positive real numbers such that $xyz=1$. Prove that $$\frac x{y^3+2}+\frac y{z^3+2}+\frac z{x^3+2}\ \geqslant\ 1.$$

Let $x,y,z$ be positive real numbers such that $xyz=1$. Prove that $$\frac x{y^3+2}+\frac y{z^3+2}+\frac z{x^3+2}\ \geqslant\ 1.$$

Jun 22, 2019 #3 topsquark Well-known member MHB Math Helper Aug 30, 2012 1,120 lfdahl said: A hint ... Spoiler is requested Click to expand... Niiiiice. -Dan