Question

If the product of two consecutive even integers is 288, how do you find the integers?

Answer 1

`288 = (n-1)(n+1) = n^2-1^2 = n^2 - 1`

[[ using the difference of squares identity `a^2-b^2 = (a-b)(a+b)` ]]

Then `n^2 = 288 + 1 = 289 = 17^2`

So `n = +-sqrt(17^2) = +-17`

and the pair of integers is 16 and 18 or -18 and -16.