यदि `(a+bx)/(a-bx)=(b+cx)/(b-cx)=(c+dx)/(c-dx)=(xne0)` तो दिखाइए कि a, b, c, G.P. में है|

Explanation

यदि `(a+bx)/underset((i))(a-bx)=(b+cx)/underset((ii))(b-cx)=(c+dx)/underset((iii))(c-dx)" ".......(1)`
(i) और (ii) से, `(a+bx)/(a-bx)=(b+cx)/(b-cx)`
`implies(2a)/(2bx)=(2b)/(2cx)" "` [by componendo and dividendo]
`implies(a)/(b)=(b)/(c)`
`implies(b)/(a)=(c)/(b)`
(ii) और (iii) से, `(b+cx)/(b+x)=(c+dx)/(c-dx)" "......(2)`
`implies(2b)/(2cx)=(2c)/(2dx)" "` [by componedo and dividendo]
`implies(b)/(c)=(c)/(d)`
`implies(c)/(b)=(d)/(c)`
(2) और (3) से, हमें मिलता है `(b)/(a)=(c)/(b)=(d)/(c)" "......(3)`
अतः a, b, c, d G.P. में से,