MathDB

An inequality

Source: Gulf MO 2012, Problem 2

June 14, 2012

inequalitiesparameterizationalgebra proposedalgebra

Problem Statement

Prove that if

a, b, c

are positive real numbers, then the least possible value of

6a^3 + 9b^3 + 32c^3 + \frac{1}{4abc}

6

. For which values of

a, b

and

c

is equality attained?