IMO 2008 Shortlist A2
(a) Prove the inequality x2 (x − 1)2 + y2 (y − 1)2 + z2 (z − 1)2 ≥ 1 for real numbers x,y,z 6= 1 satisfying the conditio...
Category: Algebra
Problem
(a) Prove the inequality x2 (x − 1)2 + y2 (y − 1)2 + z2 (z − 1)2 ≥ 1 for real numbers x,y,z 6= 1 satisfying the condition xyz = 1. (b) Show that there are infinitely many triples of rational numbers x, y, z for which this inequality turns into equality.