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If `a`, `b`, `c` are real numbers forming an `A.P.` and `3+a`, `2+b`, `3+c` are in `G.P.` , then minimum value of `ac` is

A

`-4`

B

`-6`

C

`3`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `:. (2+b)^(2)=(3+a)(3+c)` ,brgt `:. 4+b^(2)+4b=9+3(a+c)+ac`
`:.4+b^(2)+4b=9+6b+ac` ,brgt `:.ac=b^(2)-2b-5=(b-1)^(2)-6`
`:.ac ge -6`
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