Sequence And Series Question 299
Question: If $ a,\ b,\ c $ are the positive integers, then $ (a+b)(b+c)(c+a) $ is
[DCE 2000]
Options:
A) $ <8abc $
B) $ >8abc $
C) $ =8abc $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
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 $ .
BETA
