Problem

Source: Czech and Slovak Olympiad 2018, National Round, Problem 2

Tags: algebra, national olympiad



Let x,y,z be real numbers such that the numbers 1|x2+2yz|,1|y2+2zx|,1|z2+2xy|are lengths of sides of a (non-degenerate) triangle. Determine all possible values of xy+yz+zx.