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If a,b,c are positive numbers and `a+b+=c1,` then the maximum value of `(1-a) (1-b) (1-c)` is :

A

`(1)/(27)`

B

`(8)/(27)`

C

`(4)/(27)`

D

9

Text Solution

Verified by Experts

The correct Answer is:
B
Using `G.M.leA.M.,` we have
`{(1-a)(1-b)(1-c)}^(1//3)le(1-a+1-b+1-c)/(3)`
`implies" "(1-a)(1-b)(1-c)le(8)/(27)`
Hence, the greatest value is `(8)/(27)`
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