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" if " |{:(1,,1,,1),(a,,b,,c),(bc,,ca,,...

`" if " |{:(1,,1,,1),(a,,b,,c),(bc,,ca,,ab):}|=|{:(1,,1,,1),(a,,b,,c),(a^(3),,b^(3),,c^(3)):}|` where a,b,c are distinct positive reals then the possible values of abc is`//`are

A

`(1)/(18)`

B

`(1)/(63)`

C

`(1)/(27)`

D

`(1)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
we have
`(a-b)(b-c)(c-a)=(a-b)(b-c)(c-a)(a+b+c)`
`rArr a+b+c =1`
As a , b, and c are positive
using `AM gt GM` we get
`(a+b+c)/(3) gt (abc)^(1/3)`
`:. Abc lt (1)/(27)`
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