IMO 1966 LL YUG46

Let

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IMO 1966 LL YUG46

Origin: YUG

Problem

Let f(a, b, c) = |b −a| |ab|

  • b + a ab −2 c
  • |b −a| |ab|
  • b + a ab
  • 2 c . Prove that f(a, b, c) = 4 max{1/a, 1/b, 1/c}.