Question 80
Let $a, b, c$ be three strictly positive real numbers. Show that
$$
\frac{a^{4}+1}{b^{3}+b^{2}+b}+\frac{b^{4}+1}{c^{3}+c^{2}+c}+\frac{c^{4}+1}{a^{3}+a^{2}+a} \geqslant 2
$$
$$
\frac{a^{4}+1}{b^{3}+b^{2}+b}+\frac{b^{4}+1}{c^{3}+c^{2}+c}+\frac{c^{4}+1}{a^{3}+a^{2}+a} \geqslant 2
$$