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2(a^3 + b^3 + c^3 + abc) >= (a+b)(b + c)(c + a) for a,b,c>0

Source: 2011 Saudi Arabia Pre-TST November 2.2

January 1, 2022
algebrainequalities

Problem Statement

Prove that for any positive real numbers a,b,ca, b, c, 2(a3+b3+c3+abc)≥(a+b)(b+c)(c+a)2(a^3 + b^3 + c^3 + abc) \ge (a+b)(b + c)(c + a).
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