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If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx...

If `(a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0)` , then show that `a ,\ b ,\ c\ a n d\ d` are in G.P.

Text Solution

Verified by Experts

It is given that
`(a+bx)/(a-bx)=(b+cx)/(b-cx)=(c+dx)/(c-dx)=lamda`(say)
Now, `(a+bx)/(a-bx)=lamda/1=lamda`
or `((a+bx)-(a-bx))/((a+bx)+(a-bx))=(lamda-1)/(lamda+1)`
or `(bx)/a=(lamda-1)/(lamda+1)`
or `b/a=((lamda-1))/(x(lamda+1))`
Thus,a,b,c,d are in G.P.
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