Let $a, b, c \ge 0$ so that $ab + bc + ca = 3$. Prove that: $$\frac{a}{a^2+7}+\frac{b}{b^2+7}+\frac{c}{c^2+7}\le \frac38$$
Source: 2018 Romanian NMO grade VIII P4
Tags: algebra, inequalities
Let $a, b, c \ge 0$ so that $ab + bc + ca = 3$. Prove that: $$\frac{a}{a^2+7}+\frac{b}{b^2+7}+\frac{c}{c^2+7}\le \frac38$$