Question

If `(3x + 4y)/(3u + 4v) = (3x - 4y)/(3u - 4v)`, then show that `x/y = u/v`.

Answer 1

We have
`(3x + 4y)/(3u + 4v) = (3x - 4y)/(3u - 4v)  ...["Applying alternendo"]`

`(3x + 4y)/(3u - 4v) = (3x + 4y)/(3u - 4v)`   ...[By componendo and dividendo]
`(3x + 4y + 3x - 4y)/(3x + 4y - 3x + 4y) = (3u + 4v + 3u - 4v)/(3u + 4v - 3u + 4v)`
⇒ `(6x)/(8y) = (6u)/(8v)`
⇒  `x/y = u/v`.
Hence proved.