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IrMO 2021 Problem 9

  • Paper 2

Suppose the real numbers a,A,b,Ba, A, b, B satisfy the inequalities: ∣A−3a∣≤1−a  ,  ∣B−3b∣≤1−b|A - 3a| \le 1 - a\,\, , \,\, |B -3b| \le 1 - b , and a,ba, b are positive. Prove that ∣AB3−3ab∣−3ab≤1−ab.\left|\frac{AB}{3}- 3ab\right | - 3ab \le 1 - ab.

Dataset text AI-MO AoPS. Quoted with source.

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