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Unsolved Challenge Challenge Problem #7: Σ(x/(y^3+2))≥1

Olinguito

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

lfdahl

Well-known member
Nov 26, 2013
719
A hint ...

is requested (Giggle)
 

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,120