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Question

If a,b,c are the positive integers, then (a+b)(b+c)(c+a) is

A
= 8 abc
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B
< 8 abc
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C
None of these
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D
> 8 abc
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Solution

The correct option is D > 8 abc
Since A.M > G.M., we have
a+b2>ab,b+c2>bc and a+c2>ac.
Multiplying these inequalities, we get
(a+b)(b+c)(c+a)>8abc.

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