# Nice inequality (Author: Van Khea 06/2015)

Let $a, b, c$ be positive real numbers such that $abc=1$.
Prove that:
$\displaystyle \biggl(\frac{a}{1+b}\biggl)^{3/5}+\biggl(\frac{b}{1+c}\biggl)^{3/5}+\biggl(\frac{c}{1+a}\biggl)^{3/5}\geq \frac{3}{2^{3/5}}$