Question 80
Let $x$, $y$, $z$, $t$ be positive real numbers such that $xyzt = 1$ and
$$
\frac{x}{y} + \frac{y}{z} + \frac{z}{t} + \frac{t}{x} \leq x + y + z + t.
$$
Prove that
$$
\frac{y}{x} + \frac{z}{y} + \frac{t}{z} + \frac{x}{t} \geq x + y + z + t.
$$
$$
\frac{x}{y} + \frac{y}{z} + \frac{z}{t} + \frac{t}{x} \leq x + y + z + t.
$$
Prove that
$$
\frac{y}{x} + \frac{z}{y} + \frac{t}{z} + \frac{x}{t} \geq x + y + z + t.
$$