Question

Show, that a, b, c, d are in proportion if:
(6a + 7b) : (6c + 7d) : : (6a - 7b) : (6c - 7d)

Answer 1

We have,
`a/c = c/d`
`("Both sides are multiplied by" (6)/(7))`
⇒ `(6a)/(7b) = (6c)/(7d)`
Applying componendo and dividendo
`(6a + 7b)/(6a - 7b) = (6c + 7d)/(6c - 7d)`
Applying alternendo
`(6a + 7b)/(6c + 7d) = (6a - 7b)/(6c - 7d)`
(6a + 7b ) : (6c + 7d) :: (6a - 7b) (6c - 7d).