Question

If (6a + 5b) (6c − 5d) = (6a − 5b) (6c + 5d), prove that a, b, c, d are in proportion.

Answer 1

We have given that:

⇒ `(6a + 5b)/(6c − 5d) = (6a − 5b)/(6c + 5d)`

⇒ `(6a + 5b)/(6a − 5b) = (6c − 5d)/(6c + 5d)`

Apply the Componendo and Dividendo:

⇒ `((6a + 5b) + (6a − 5b))/((6a + 5b) - (6a − 5b)) = ((6c + 5d) + (6c − 5d))/((6c + 5d) - (6c − 5d))`

⇒ `(12a)/(10b) = (12c)/(10d)`

⇒ `(6a)/(5b) = (6c)/(5d)`   ...(dividing by 2)

⇒ `a/b = c/d`

Hence proved.