11 - Inequalities

Let $a, b, c$ be positive real numbers such that $abc = 1$.  

Prove that

$\dfrac{a}{ca + 1} + \dfrac{b}{ab + 1} + \dfrac{c}{bc + 1} ≤ \dfrac{1}{2}(a^2 + b^2 + c^2 )$

Proposed by Sayan Das, Kolkata, India 

 Διασκεδαστικά Μαθηματικά    www.eisatopon.blogspot.com