Question

If a : b = c : d, show that (2a - 7b) (2c + 7d) = (2c - 7d) (2a + 7b).

Answer 1

We have
a: b = c : d
`a/b = c/d`
⇒ `(2a)/(7b) = (2c)/(7d)     ...["Multiplying both side" 2/7]`
`["Using componendo and dividendo"]`
`(2a + 7b)/(2a - 7b) = (2c + 7d)/(2c - 7d)`   ...[By cross multiplication]
⇒  (2a - 7b) (2c + 7d) = (2a + 7b) (2c - 7d).
Hence proved.