IMO 2010 Shortlist A8

Given six positive numbers a,b,c,d,e,f such that a b c d e f. Let a c e S and b d f T. Prove that 2ST ¡ b 3pS Tq Spbd ...

IMO 2010 Shortlist A8

Category: Algebra

Problem

Given six positive numbers a,b,c,d,e,f such that a b c d e f. Let a c e S and b d f T. Prove that 2ST ¡ b 3pS Tq Spbd bf dfq Tpac ae ceq  . (1) (South Korea)