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If a,b,c are in AP and (a+2b-c)(2b+c-a)...

If a,b,c are in AP and `(a+2b-c)(2b+c-a)(c+a-b)=lambdaabc`, then `lambda` is

A

1

B

2

C

4

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`:.a,b,c` are in AP.
`:. 2b=a+c" " "…..(i)"`
Now, `(a+2b-c)(2b+c-a)(c+a-b)`
`(a+a+c-c)(a+c+c-a)(2b-b)" " [" from Eq.(i) "]`
`=(2a)(2c)(b)=4abc`
`:. Lambda =4`.
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