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If a ,b, c ,d are in G.P, then (b-c)^2+(...

If `a ,b, c ,d` are in G.P, then `(b-c)^2+(c-a)^2+(d-b)^2` is equal to

A

`(a-d)^2`

B

`(a d)^2`

C

`(a+d)^2`

D

`(a//d)^2`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `a ,b, c ,d` are in G.P

`r` be common ratio

`b=ar, c=ar^2, d=ar^3`

To simplify :`(b-c)^2+(c-a)^2+(d-b)^2`

`=(ar-ar^2)^2+(ar^2-a)^2+(ar^3-ar)^2`

`=a^2r^2(1-r)^2+a^2(r^2-1)^2+a^2r^2(r^2-1)^2`

`=a^2(r^6-2r^3+1)`

...
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