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.
Accepted Solution
A:
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!