IMO 2009 Shortlist A4

Let a, b, c be positive real numbers such that ab + bc + ca ≤ 3abc. Prove that r a2 + b2 a + b + r b2 + c2 b + c + r c2 ...

imomathematicsolympiadshortlistalgebra

IMO 2009 Shortlist A4

Category: Algebra

Problem

Let a, b, c be positive real numbers such that ab + bc + ca ≤ 3abc. Prove that r a2 + b2 a + b + r b2 + c2 b + c + r c2 + a2 c + a

  • 3 ≤ √ √ a + b + √ b + c + √ c + a  .