IMO 2016 Shortlist A1

Let a,b and c be positive real numbers such that min{ab,bc,ca} ⩾ 1. Prove that » (a2 + 1)(b2 + 1)(c2 + 1) ⩽ Ç a + b + c ...

imomathematicsolympiadshortlistalgebra

IMO 2016 Shortlist A1

Category: Algebra

Problem

Let a,b and c be positive real numbers such that min{ab,bc,ca} ⩾ 1. Prove that » (a2 + 1)(b2 + 1)(c2 + 1) ⩽ Ç a + b + c å2