SOLUTION: This problem is not from my book. I have tried to answer it but don't feel I am correct, and I need every point possible to pass this course. Problem What is the minimum product

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Question 81046: This problem is not from my book. I have tried to answer it but don't feel I am correct, and I need every point possible to pass this course.
Problem
What is the minimum product of two numbers whose difference is 4? What are the numbers?
Here is what I have done.
n(n+1)=-4
n^2 + n = -4
n^2 + n - 4 = 0
(n+1)(n-4)
The numbers are 1, -4, the minimum product is -4
Thank you so much for your help. Like I said I don.t think my solution is correct.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
if the difference is 4 (not 5), then the numbers are n and n+4 (not n+1) ... so y=n(n+4)

setting y=0 gives n=0 and n=-4 ... the minimum value for y is midway between these values (on the axis of symmetry) at n=-2

so the numbers are -2 and 2, and the product (which you did find) is -4