Question 114
Show that for the positive $x$, $y$, $z$ the following inequality holds:
$$
\frac{x^8+1}{x^4} + \frac{y^8+1}{y^4} + \frac{z^8+1}{z^4} \geq 2 \cdot \left( \frac{x}{z} + \frac{z}{y} + \frac{y}{x} \right).
$$
$$
\frac{x^8+1}{x^4} + \frac{y^8+1}{y^4} + \frac{z^8+1}{z^4} \geq 2 \cdot \left( \frac{x}{z} + \frac{z}{y} + \frac{y}{x} \right).
$$