Question 26
Let $a, b, c$ be real numbers, representing the side lengths of a triangle. Prove that
$$
\sqrt[3]{(a^2 + bc)(b^2 + ca)(c^2 + ab)} \gt \frac{a^2 + b^2 + c^2}{2}.
$$
$$
\sqrt[3]{(a^2 + bc)(b^2 + ca)(c^2 + ab)} \gt \frac{a^2 + b^2 + c^2}{2}.
$$