Question 122
Show that for positive numbers $x, y, z, t$ the following inequality holds:
$$
\frac{x^8+1}{x^4} + \frac{y^8+1}{y^4} + \frac{z^8+1}{z^4} + \frac{t^8+1}{t^4} \ge 2 \cdot \left( \frac{x}{y} + \frac{y}{z} + \frac{z}{t} + \frac{t}{x} \right).
$$
$$
\frac{x^8+1}{x^4} + \frac{y^8+1}{y^4} + \frac{z^8+1}{z^4} + \frac{t^8+1}{t^4} \ge 2 \cdot \left( \frac{x}{y} + \frac{y}{z} + \frac{z}{t} + \frac{t}{x} \right).
$$