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.

Answer

N/a

Explanation

Given ,
`(a + bx)/(a - bx)= (b + cx)/(b - cx) = (c + dx)/(c - dx)`
From componendo / dividendo rule
`(a + bx + a - bx)/(a + bx - a + bx) = (b + cx + b - cx)/(b + cx - b + cx)`
`= (c + dx + c - dx)/(c + dx - c + dx)`
`rArr` `(2a)/(2bx) = (2b)/(2cx) = (2c)/(2dx)`
`rArr` `(a)/(b) = (b)/(c) = (c)/(d) rArr a, b, c, d ` are in G.P.
Hence Proved.