Problem

Source: Moldova TST 2018, b6

Tags: inequalities, three variable inequality, algebra



Let $a,b,c$ be positive real numbers such that $a+b+c=3$. Show that $$\frac{a}{1+b^2}+\frac{b}{1+c^2}+\frac{c}{1+a^2}\geq \frac{3}{2}.$$