If a- b- c are the positive integers- then a-bb-cc-a isA- 8 abcC- None of theseD- -8 abc

The correct option is B gt; 8 abcSince A.M gt; G.M., we have a+b/2 gt; √(ab), b+c/2 gt; √(bc) and a+c/2 gt; √(ac). Multiplying these inequalities, ...

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Standard XII

Mathematics

Domain

If a, b, c ar...

Question

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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= 8 abc

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None of these

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Solution

The correct option is B > 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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If a,b,c are the positive integers, then (a+b)(b+c)(c+a) is

The correct option is B > 8 abcSince 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.

The correct option is B > 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
$(a + b) (b + c) (c + a) > 8 a b c .$