Problem

Source: Indian TST Day 2 Problem 2

Tags: inequalities, triangle inequality, algebra unsolved, algebra



For j=1,2,3 let xj,yj be non-zero real numbers, and let vj=xj+yj.Suppose that the following statements hold: x1x2x3=y1y2y3 x21+x22+x23=y21+y22+y23 v1,v2,v3 satisfy triangle inequality v21,v22,v23 also satisfy triangle inequality. Prove that exactly one of x1,x2,x3,y1,y2,y3 is negative.