IMO 2019 Shortlist A2

Let u1, u2, ..., u2019 be real numbers satisfying u1 u2 ¨¨¨ u2019 “ 0 and u2 1 u2 2 ¨¨¨ u2 2019 “ 1. Let a “ minpu1,u2,....

imomathematicsolympiadshortlistalgebra

IMO 2019 Shortlist A2

Category: Algebra

Problem

Let u1, u2, ..., u2019 be real numbers satisfying u1 u2 ¨¨¨ u2019 “ 0 and u2 1 u2 2 ¨¨¨ u2 2019 “ 1. Let a “ minpu1,u2,...,u2019q and b “ maxpu1,u2,...,u2019q. Prove that ab ď ´ . (Germany)