The product of two consecutive intergers is 240. What are the two intergers?

Question

If you open a book to two page numbers, one on each side and the total of the two page numbers is 240, what are the two page numbers?

Answer 1

x(1)*x(2) = 240

x(2) = x(1) + 1

x(1)((x(1) + 1)) = 240

(x(1))^2 + x(1) - 240 = 0

            - 1 + sqrt(1^2 - 4( -240)         -1 + sqrt 961

x(1) = ----------------------------------- =  --------------------

                   2                                           2

X(1) = ( - 1 + 31)/2 = 15

x(2) = 15 + 1 = 16

15 *16 = 240