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(a - b)(b - c)(a- c)<= 2 if 0 <=a, b, c <= 2.

Source: 2023 Austrian Regional Competition For Advanced Students p1

March 26, 2024
inequalitiesalgebra

Problem Statement

Let aa, bb and cc be real numbers with 0≤a,b,c≤20 \le a, b, c \le 2. Prove that (a−b)(b−c)(a−c)≤2.(a - b)(b - c)(a- c) \le 2. When does equality hold?
(Karl Czakler)
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