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min of f(a, b, c) = (a + b)^4 + (b + c)^4 + (c + a)^4 -477 (a^4 + b^4 + c^4)

Source: Indian Postal Coaching 2009 set 1 p1

May 26, 2020
algebramininequalities

Problem Statement

Find the minimum value of the expression f(a,b,c)=(a+b)4+(b+c)4+(c+a)4−47(a4+b4+c4)f(a, b, c) = (a + b)^4 + (b + c)^4 + (c + a)^4 - \frac47 (a^4 + b^4 + c^4), as a,b,ca, b, c varies over the set of all real numbers
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