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.
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.
