IMO 2008 Shortlist A7

Prove that for any four positive real numbers a,b,c,d the inequality (a − b)(a − c) a + b + c + (b − c)(b − d) b + c + d...

imomathematicsolympiadshortlistalgebra

IMO 2008 Shortlist A7

Category: Algebra

Problem

Prove that for any four positive real numbers a,b,c,d the inequality (a − b)(a − c) a + b + c + (b − c)(b − d) b + c + d + (c − d)(c − a) c + d + a + (d − a)(d − b) d + a + b ≥ 0 holds. Determine all cases of equality.