Question 8
Show that
$$
a + b + c + \sqrt{3} \geq 8abc \left( \frac{1}{a^2 + 1} + \frac{1}{b^2 + 1} + \frac{1}{c^2 + 1} \right)
$$
for all positive real numbers $a, b, c$ satisfying $ab + bc + ca \leq 1$.
$$
a + b + c + \sqrt{3} \geq 8abc \left( \frac{1}{a^2 + 1} + \frac{1}{b^2 + 1} + \frac{1}{c^2 + 1} \right)
$$
for all positive real numbers $a, b, c$ satisfying $ab + bc + ca \leq 1$.