MCQ
If $a,\;b,\;c$ are the positive integers, then $(a + b)(b + c)(c + a)$ is
- A$ < 8abc$
- ✓$ > 8abc$
- C$ = 8abc$
- DNone of these
✓
Answer
Correct option: B.
$ > 8abc$
b
(b) Since $A.M. > G.M.$, we have
(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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