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Question

Let a, b, c be positive real numbers. Find the minimum value of (a + b)(a + c)(b + c)abc.

Accepted Answer

By AM-GM, align* a + b 2 ab, a + c 2 ac, b + c 2 bc, align*so (a + b)(a + c)(b + c)abc 2 ab 2 ac 2 bcabc = 8.Equality occurs when a = b = c, so the minimum value is 8.