Problem

Source: Turkey TST 2020 Day 3 P8

Tags: inequalities, algebra, Turkey, High school olympiad



Let $x,y,z$ be real numbers such that $0<x,y,z<1$. Find the minimum value of: $$\frac {xyz(x+y+z)+(xy+yz+zx)(1-xyz)}{xyz\sqrt {1-xyz}}$$