Question 98
Show that
$$
\frac{(b+c)(a^4 - b^2c^2)}{ab + 2bc + ca} + \frac{(c+a)(b^4 - c^2a^2)}{bc + 2ca + ab} + \frac{(a+b)(c^4 - a^2b^2)}{ca + 2ab + bc} \geq 0
$$
for all positive real numbers $a, b, c$.
$$
\frac{(b+c)(a^4 - b^2c^2)}{ab + 2bc + ca} + \frac{(c+a)(b^4 - c^2a^2)}{bc + 2ca + ab} + \frac{(a+b)(c^4 - a^2b^2)}{ca + 2ab + bc} \geq 0
$$
for all positive real numbers $a, b, c$.