IMO 2010 Shortlist A2

Let the real numbers a,b,c,d satisfy the relations a b c d 6 and a2 b2 c2 d2 12. Prove that 36 ¨4pa3 b3 c3 d3 qpa4 b4...

imomathematicsolympiadshortlistalgebra

IMO 2010 Shortlist A2

Category: Algebra

Problem

Let the real numbers a,b,c,d satisfy the relations a b c d 6 and a2 b2 c2 d2 12. Prove that 36 ¨4pa3 b3 c3 d3 qpa4 b4 c4 d4 q¨48. (Ukraine)