Question

If `(8a - 5b)/(8c - 5a) = (8a + 5b)/(8c + 5d)`, prove that `a/b = c/d`

Answer 1

`(8a - 5b)/(8c - 5a) = (8a + 5b)/(8c + 5d)`

⇒ `(8a + 5b)/(8a - 5b) = (8c + 5b)/(8c - 5d)`  ...(using alternendo)
Applying componendo and dividendo,
`(8a + 5b + 8a - 5b)/(8a + 5b - 8a + 5b) = (8c + 5d + 8c - 5c)/(8c + 5d - 8c + 5d)`

∴ `(16a)/(10b) = (16c)/(10d)`

⇒ `a/b = c/d       ...("Dividing by" 16/10)`
Hence proved.