Question

If `(3x + 4y)/(3a + 4b) = (3x - 4y)/(3a - 4b),` prove that `x/y = a/b`.

Answer 1

We have given that:

⇒ `(3x + 4y)/(3a + 4b) = (3x - 4y)/(3a - 4b)`

⇒ (3x + 4y) (3a − 4b) = (3x − 4y) (3a + 4b)

Apply Componendo and Dividendo:

⇒ `((3x + 4y) + (3x - 4y))/((3x + 4y) - (3x - 4y)) = ((3a + 4b) + (3a - 4b))/((3a + 4b) - (3a - 4b))`

⇒ `(6x)/(8y) = (6a)/(8b)`

⇒ `(6x)/(8y) xx 8/6 = (6a)/(8b) xx 8/6`

⇒ `x/y = a/b`

Hence proved.