SOLUTION: The difference between two integers is three and their product is 40. What are the two numbers? Thank you!!

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Question 954964: The difference between two integers is three and their product is 40. What are the two numbers?
Thank you!!
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
x and y are integers
x-y=3
x=y+3
xy=40 Substitute for x
%28y%2B3%29y=40
y%5E2%2B3y=40 Subtract 40 from each side.
y%5E2%2B3y-40=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 1y%5E2%2B3y%2B-40+=+0) has the following solutons:

y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A1%2A-40=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+169+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%283%29%2Bsqrt%28+169+%29%29%2F2%5C1+=+5
y%5B2%5D+=+%28-%283%29-sqrt%28+169+%29%29%2F2%5C1+=+-8

Quadratic expression 1y%5E2%2B3y%2B-40 can be factored:
1y%5E2%2B3y%2B-40+=+1%28y-5%29%2A%28y--8%29
Again, the answer is: 5, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-40+%29

y=5 ANSWER 1: One of the integers is 5.
x=y+3=5+3=8 ANSWER 2: The other integer is 8.
CHECK:
xy=40
(8)(5)=40
40=40