Question 10
Given real positive numbers $x_1, \dots, x_n$ ($n \ge 3$) such that $x_1 \cdot \dots \cdot x_n = 1$, prove that
$$
\frac{x_1^8}{(x_1^4 + x_2^4)x_2} + \frac{x_2^8}{(x_2^4 + x_3^4)x_3} + \dots + \frac{x_n^8}{(x_n^4 + x_1^4)x_1} \ge \frac{n}{2}.
$$
(I. Voronovich)
$$
\frac{x_1^8}{(x_1^4 + x_2^4)x_2} + \frac{x_2^8}{(x_2^4 + x_3^4)x_3} + \dots + \frac{x_n^8}{(x_n^4 + x_1^4)x_1} \ge \frac{n}{2}.
$$
(I. Voronovich)