Question

The difference of the squares of two positive consecutive even integers is 12. Find the integers. Use the fact that, if x represents an even integer, then x + 2 represents the next consecutive even integer

Answer 1

2 and 4.

Explanation:

(x+2)^2 - x^2 = 12

x^2 + 4x + 4 - x^2 = 12

4x + 4 = 12

4x = 8

x = 2.

Hence the integers are 2 and 4.