Question 86
Let $a$, $b$, $c$ be positive numbers such that $ab + bc + ca = 3$. Prove that
$$
\frac{a}{\sqrt{a^{3}+5}} + \frac{b}{\sqrt{b^{3}+5}} + \frac{c}{\sqrt{c^{3}+5}} \leq \frac{\sqrt{6}}{2}
$$
$$
\frac{a}{\sqrt{a^{3}+5}} + \frac{b}{\sqrt{b^{3}+5}} + \frac{c}{\sqrt{c^{3}+5}} \leq \frac{\sqrt{6}}{2}
$$