SOLUTION: If the difference between the squares of two consecutive even integers is the same as four less then the product of the integers what is one of the integers?

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Question 331857: If the difference between the squares of two consecutive even integers is the same as four less then the product of the integers what is one of the integers?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two integers, x, (x+2)
:
If the difference between the squares of two consecutive even integers is
the same as four less then the product of the integers
(x+2)^2 - x^2 = x(x+2) - 4
:
x^2 + 4x + 4 - x^2 = x^2 + 2x - 4
:
4x + 4 = x^2 + 2x - 4
:
0 = x^2 + 2x - 4x - 4 - 4
Solve a quadratic equation
x^2 - 2x - 8 = 0
Factors to
(x-4)(x+2) = 0
Two solutions
x = 4, 6 are the two integers they want
and
x = -2, 0; not sure if these qualify
:
:
See if this flies
4, 6
6^2 - 4^2 = 4(6) - 4
36 - 16 = 24 - 4; OK
and
-2, 0
0 - 4 = 0 - 4;