The difference of two positive integers is 9 and the differe

The difference of two positive integers is 9 and the difference of their squares is 189. What is the sum of the numbers ?

Solution

let both integerts be n and m

==> n - m = 9 ........(1)

The difference of their square is 189

==> n^2 - m^2 = 189

We knoiw that n^2 - m^2 = (n-m)(n+m)

==> (n-m)(n+m) = 189

but n-m = 0

==> 9(n+m) = 189

Now divide by 9:

==> n+m = 189/9

==: n + m = 21 ...........(2)

Now add (1) and (2):

==> 2n = 30

==> n= 15

==> n+m = 21

==> m= 21- n= 21- 15

==> m= 6