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 and d are in G.P.

Explanation

We have `(a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)`


& We want to show that a, b, c and d are in G.P.


Taking


`(a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)`


Applying componendo dividendo


`(a+b x+a-bx)/(a+bx-a+b x)=(b+c x+b-cx)/(b+cx-b+c x)=(c+dx+c-dx)/(c+dx-c+dx)`


`(2a)/(2bx)=(2b)/(2cx)=(2c)/(2dx)`


`(a)/(bx)=(b)/(cx)=(c)/(dx)`


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