#### Question

If (7a + 8b) (7c – 8d) = (7a – 8b) (7c + 8d), prove that a: b = c: d.

#### Solution

Given `(7a + 8b)/(7c – 8d) = (7a – 8b)/(7c + 8d)`

Applying componendo and dividendo

`(7a + 8b + 7a - 8b)/(7a + 8b - 7 + 8b) = (7c + 8d + 7c - 8d)/(7c + 8d - 7c - 8d)`

`=> (14a)/(16b) = (14c)/(16d)`

`=> a/b = c/d`

Hence a : b = c : d

Is there an error in this question or solution?

Solution If (7a + 8b) (7c – 8d) = (7a – 8b) (7c + 8d), Prove that A: B = C: D. Concept: Componendo and Dividendo Properties.