MathDB
largest possible k?

Source: Own. IMO 2022 Malaysian Training Camp 2

March 14, 2022
algebrainequalitiesInequality

Problem Statement

Let a,b,c,a, b, c, be nonnegative reals with a+b+c=3 a+b+c=3 , find the largest positive real k k so that for all a,b,c,a,b,c, we have a2+b2+c2+k(abc−1)≥3 a^2+b^2+c^2+k(abc-1)\ge 3
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