Are there four real numbers $a, b, c, d$ for every three positive real numbers $x, y, z$ with the property $ad + bc = x$, $ac + bd = y$, $ab + cd = z$ and one of the numbers $a, b, c, d$ is equal to the sum of the other three?
Problem
Source: Czech-Polish-Slovak Junior Match 2018, individual p1 CPSJ
Tags: Sum, system of equations, algebra