IMO 2009 Shortlist A2

Let a, b, c be positive real numbers such that a + b + c = a + b + c. Prove that (2a + b + c)2 + (2b + c + a)2 + (2c + a...

imomathematicsolympiadshortlistalgebra

IMO 2009 Shortlist A2

Category: Algebra

Problem

Let a, b, c be positive real numbers such that a + b + c = a + b + c. Prove that (2a + b + c)2 + (2b + c + a)2 + (2c + a + b)2 ≤ .