Let $a, b, c, d$ be real numbers satisfying the system

$a / b + b / c + c / d + d / a = 6$

$a / c + b / d + c / a + d / b = 8$

What values can the expression $a / b + c / d$ take?
Let $x=a / b+c / d, y=b / c+d / a$, then $x+y=6, x y=a / c+b / d+c / a+d / b=8$. Therefore, $x$ and $y$ are the roots of the quadratic equation $t^{2}-6 t+8=0$, that is, $x=2$ or $x=4$.

These values are achieved, for example, at $(a, b, c, d)=(2+\sqrt{3}, 2+\sqrt{3}, 1,1)$ and $(2+\sqrt{3}, 1,1,2+\sqrt{3})$.

## Problem