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If a, b are postitive real numbers such ...

If a, b are postitive real numbers such that ab=1, then the least value of the expression `(1+a)(1+b)` is

A

2

B

3

C

4

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `ab=1impliesb=(1)/(a)`
`:." "(1+a)(1+b)=(1+a)(1+(1)/(a))`
`implies" "(1+a)(1+(1)/(a))=2+a+(1)/(a)ge2+2=4" "[because a+(1)/(a)ge2]`
Hence, the least value of `(1+a)(1+b)` is 4.
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