Question 60
Let $a$, $b$, $c$ be positive real numbers such that $a^{2} + b^{2} + c^{2} = 48$. Prove
$$
a^{2} \sqrt{2 b^{3} + 16} + b^{2} \sqrt{2 c^{3} + 16} + c^{2} \sqrt{2 a^{3} + 16} \leq 24^{2}
$$
When does equality hold?
$$
a^{2} \sqrt{2 b^{3} + 16} + b^{2} \sqrt{2 c^{3} + 16} + c^{2} \sqrt{2 a^{3} + 16} \leq 24^{2}
$$
When does equality hold?