Question

Find 2 consecutive positive even integers such that the product of the 1st and 2nd is 2 less than 5 times the 3rd. Use an algebraic solution.

Answer 1

Assume the smaller one is x, then the other ones will be x+2 and x+4

x(x+2) + 2 = 5(x+4)

x^2 + 2x - 5x - 18 = 0

-> x^2 - 3x - 18 = 0

-> (x-6)(x+3) = 0

-> x = 6 or -3, since x must be positive, then x = 6

So the numbers are: 6, 8, 10