IMO 2006 Shortlist A5

Let a,b,c be the sides of a triangle. Prove that √ b + c − a √ b + √ c − √ a + √ c + a − b √ c + √ a − √ b + √ a + b − c...

imomathematicsolympiadshortlistalgebra

IMO 2006 Shortlist A5

Category: Algebra

Problem

Let a,b,c be the sides of a triangle. Prove that √ b + c − a √ b + √ c − √ a + √ c + a − b √ c + √ a − √ b + √ a + b − c √ a + √ b − √ c ≤ 3. (Korea)