Find two consecutive even integers whose product is 156. What are the integers?

156

can be broken down into:

2 * 2 * 13 * 3

Well if you didn't need two EVEN integers, 12 * 13 would give you 156, however... like what already has been established, there is no numbers that are both even and will do this for you. You can try any combination of product orders with the numbers above and not ever find this kind of combo, or do what roderick did and test out the even numbers whose products are around the range.

the integers will differ by 2. so we can assume them to be x - 1 and x + 1 (where x is to be found out)

product = (x - 1) (x + 1) = 156

=> x² - 1 = 156

=> x² = 157

x is not integers! so there will be no two consecutive integers having product = 156!

I get no solution. 10 * 12 = 120, which is too little, and 12 * 14 = 168, which is too much.

Are you sure you don't mean two consecutive integers? If so, set it up this way: let n be the first integer. Then the second integer is n+1

n(n+1) = 156

n^2 + n - 156 = 0

solve the quadratic by factoring, completing the square, or quadratic formula, as I don't think they want you to guess and check.

x * (x + 2) = 156

x^2 + 2x = 156

x^2 + 2x + 1 = 157

(x + 1)^2 = 157

x + 1 = +/- sqrt(157)

x = -1 +/- sqrt(157)

No solution.

12 and 13.