If a, ;b, ;c are the positive integers, then (a + b)(b + c)(c + a… - Vidyadip

MCQ

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

A
$ < 8abc$
✓
$ > 8abc$
C
$ = 8abc$
D
None of these

✓

Answer

Correct option: B.

$ > 8abc$

b
(b) 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

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

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