Question

if `(3a + 4b)/(3c + 4d) = (3a - 4b)/(3c - 4d)` Prove that `a/b = c/d`.

Answer 1

Given `(3a + 4b)/(3c + 4d) = (3a - 4b)/(3c - 4d)`
App. alternendo = `(3a + 4b)/(3a - 4d) = (3c + 4b)/(3c - 4d)`
App. componendo and dividendo
`(3a + 4b + 3a - 4b)/(3a + 4b - 3a + 4b) = (3c + 4d + 3c - 4d)/(3c + 4d - 3c + 4d)`
∴ `(6a)/(8b) = (6c)/(8d)`
or
`a/b = c/d`
Hence proved.