Question

If a, b, c are positive real numbers such that `a+b+c=1`, then the greatest value of `(1-a)(1-b)(1-c), is
A. `(1)/(27)`
B. `(8)/(27)`
C. `(4)/(27)`
D. 9

Answer 1

Correct Answer - 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)`