IMO 2006 Shortlist A6

Determine the smallest number M such that the inequality ab(a2 − b2 ) + bc(b2 − c2 ) + ca(c2 − a2 ) ≤ M a2 + b2 + c2 2 ...

imomathematicsolympiadshortlistalgebra

IMO 2006 Shortlist A6

Category: Algebra

Problem

Determine the smallest number M such that the inequality ab(a2 − b2 ) + bc(b2 − c2 ) + ca(c2 − a2 ) ≤ M a2

  • b2
  • c2 2 holds for all real numbers a, b, c. (Ireland)