Question 26
Let $ABC$ be a scalene triangle with $BC = a$, $AC = b$ and $AB = c$, where $a$, $b$, $c$ are positive integers. Prove that
$$
\left|a b^{2} + b c^{2} + c a^{2} - a^{2} b - b^{2} c - c^{2} a\right| \geq 2
$$
$$
\left|a b^{2} + b c^{2} + c a^{2} - a^{2} b - b^{2} c - c^{2} a\right| \geq 2
$$