Problem

Source: RMO Hyderabad 2016 , P2 .

Tags: inequalities, algebra, inequalities proposed



Let $a,b,c$ be positive real numbers such that $$\frac{a}{1+a}+\frac{b}{1+b}+\frac{c}{1+c}=1.$$Prove that $abc \le \frac{1}{8}$.