Question

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.

Answer 1

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!