Sequence And Series Question 336
Question: If a, b, c are positive numbers, then least value of $ (a+b+c)( \frac{1}{a}+\frac{1}{b}+\frac{1}{c} ) $ is
Options:
A) 1
B) 6
C) 9
D) None
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ AM\ge HM $
$ \Rightarrow ,\frac{a+b+c}{3}\ge \frac{3}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}} $
$ \Rightarrow ,(a+b+c)( \frac{1}{a}+\frac{1}{b}+\frac{1}{c} )\ge 9 $
BETA
