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

= 8 abc

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< 8 abc

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None of these

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> 8 abc

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Solution

The correct option is D > 8 abc
Since A.M > G.M., we have
$\frac{a + b}{2} > \sqrt{a b}, \frac{b + c}{2} > \sqrt{b c}$ and $\frac{a + c}{2} > \sqrt{a c} .$
Multiplying these inequalities, we get
$(a + b) (b + c) (c + a) > 8 a b c .$

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