Question 154
Let $a, b, c$ be positive real numbers. Prove that
$$
\frac{a^4 + 1}{b^3 + b^2 + b} + \frac{b^4 + 1}{c^3 + c^2 + c} + \frac{c^4 + 1}{a^3 + a^2 + a} \ge 2.
$$
$$
\frac{a^4 + 1}{b^3 + b^2 + b} + \frac{b^4 + 1}{c^3 + c^2 + c} + \frac{c^4 + 1}{a^3 + a^2 + a} \ge 2.
$$