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

Question

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

Answer 1

The correct option is (B) > 8 abc

Since A.M > G.M., we have

\(\frac{a+b}2>\sqrt{ab},\frac{b+c}2>\sqrt{bc}\;and\;\frac{a+c}2>\sqrt{ac}.\)

Multiplying these inequalities, we get

(a+b) (b+c) (c+a) > 8abc.