Question

The product of two consecutive positive integers is 11 more than their sum, what are the integers?

Answer 1

If the integers are `m` and `m+1`, then we are given:

`mxx(m+1) = m+(m+1)+11`

That is:

`m^2+m = 2m+12`

Subtract `2m+12` from both sides to get:

`0 = m^2-m-12 = (m-4)(m+3)`

This equation has solutions `m=-3` and `m=4`

We were told that `m` and `m+1` are positive, so we can reject `m=-3`, leaving the unique solution `m=4`.

So the integers are `m=4` and `m+1=5`.