Question 2
Let $a$, $b$ and $c$ be positive real numbers such that $a b c = 8$. Prove that
$$
\frac{a^{2}}{\sqrt{\left(1+a^{3}\right)\left(1+b^{3}\right)}} + \frac{b^{2}}{\sqrt{\left(1+b^{3}\right)\left(1+c^{3}\right)}} + \frac{c^{2}}{\sqrt{\left(1+c^{3}\right)\left(1+a^{3}\right)}} \geq \frac{4}{3}
$$
$$
\frac{a^{2}}{\sqrt{\left(1+a^{3}\right)\left(1+b^{3}\right)}} + \frac{b^{2}}{\sqrt{\left(1+b^{3}\right)\left(1+c^{3}\right)}} + \frac{c^{2}}{\sqrt{\left(1+c^{3}\right)\left(1+a^{3}\right)}} \geq \frac{4}{3}
$$