Question 41
Let $a$, $b$, $c$ be positive real numbers. Prove that
$$
\sqrt{a^3 b + a^3 c} + \sqrt{b^3 c + b^3 a} + \sqrt{c^3 a + c^3 b} \geq \frac{4}{3}(ab + bc + ca)
$$
$$
\sqrt{a^3 b + a^3 c} + \sqrt{b^3 c + b^3 a} + \sqrt{c^3 a + c^3 b} \geq \frac{4}{3}(ab + bc + ca)
$$