The difference of the squares of two positive consecutive even integers is 20. find the integers. use the fact that, if x represents an even integer, then xplus 2 represents the next consecutive even integer.

If x is the first number, x+2 is the next consecutive even integer. The difference (subtraction) of their squares equals 20. Therefore:

(x+2) ²-x²=20 ... expand this:

x²+4x+4-x²=20

x²+4x+4-x²=20

4x+4=20

4x=16

x=4. Therefore the next consecutive even integer is x+2=6.

To check: 6²-4² must equal 20

36-16=20 check!