Question

The difference of the squares of two positive consecutive even integers is 28.

Find the integers. Use the fact​ that, if x represents an even​ integer, then x+2 represents the next consecutive even integer.

Answer 1

If x is the first even integer, then the next is x+2.
The difference of their squares is (x+2)^2 - x^2, and this is equal to 28.
Expanding:
x^2 + 4x + 4 - x^2 = 28
4x + 4 = 28
4x = 24
x = 6
x+2 = 8
Therefore, the two numbers are 6 and 8.