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If a+b+c=6 then the maximum value of sqr...

If `a+b+c=6` then the maximum value of `sqrt(4a+1)+sqrt(4b+1)+sqrt(4c+1)=`

A

9

B

6

C

4

D

12

Text Solution

Verified by Experts

The correct Answer is:
A
Using Cauchy-Suhwartz's inequality, we have
`{sqrt(4a+1)xx1+sqrt(4b+1)xx1+sqrt(4c+1)xx1}^(2)`
`le(1^(2)+1^(2)+1^(2)){(sqrt(4a+1")"))^(2)+(sqrt(4b+1))^(2)+(sqrt(4c+1))^(2)}`
`=(sqrt(4a+1)xxsqrt(4b+1)+sqrt(4c+1))^(2)le3{4(a+b+c)+3}`
`=(sqrt(4a+1)+sqrt(4b+1)+sqrt(4c+1))^(2)le3xx27`
`=sqrt(4a+1)+sqrt(4b+1)+sqrt(4c+1)le9`
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