Question

The product of two consecutive off integers is equal to 27 plus six times the sum of the integers . What is the largest integer?

Answer 1

15

Explanation:

x(x + 2) = 27 + 6(x + x + 2)

x^2 + 2x = 27 + 6(2x + 2)

x^2 + 2x = 27 + 12x + 12

x^2 + 2x - 12x - 12 - 27 = 0

x^2 -10x - 39 = 0

(x + 3)(x - 13) = 0

x + 3 = 0

x = -3 (extraneous solution)

x - 13 = 0

x = 13

x + 2 = 15