18.1. (GDR, 73). Find all pairs $(x ; y)$ of positive numbers at which the minimum value of the function

$$
f(x, y)=\frac{x^{4}}{y^{4}}+\frac{y^{4}}{x^{4}}-\frac{x^{2}}{y^{2}}-\frac{y^{2}}{x^{2}}+\frac{x}{y}-\frac{y}{x}
$$

is achieved, and find this minimum value.
18.1. The minimum value of the function $f(x, y)$ for $x, y > 0$ is 2, since the following relations hold:

$$
\begin{aligned}
& f(x, y)-2= \\
& =\left(\frac{x^{2}}{y^{2}}-1\right)^{2}+\left(\frac{y^{2}}{x^{2}}-1\right)^{2}+\left(\frac{x}{y}-\frac{y}{x}\right)^{2}+\left(\frac{x}{y}-2+\frac{y}{x}\right) \geqslant \\
& \geqslant \frac{(x-y)^{2}}{x y} \geqslant 0,
\end{aligned}
$$

and the equality $f(x, y)=2$ is achieved if and only if $x=y$.