SOLUTION: The difference of two numbers is 2.If the sum of their sqaures is 20,What are the numbers?

Question 906792: The difference of two numbers is 2.If the sum of their sqaures is 20,What are the numbers?
Found 2 solutions by JulietG, richwmiller:
Answer by JulietG(1812) (Show Source): You can put this solution on YOUR website!
a - b = 2
+=20
Easiest way to do this is by estimation. Since the squares added together are going to be 20, we know that the largest number must be 4 or less. Since they're two apart, the choices are:
4,2
3,1
2,0
Which of those pairs fitting the top equation also fits the bottom equation?
Only 4,2
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
a - b = 2
a^2+b^2=20
a=b+2
(b+2)^2+b^2=20
b^2+4b+4+b^2=20
2*b^2+4b+4=20
2*b^2+4b-16=0
b^2+2b-8=0
(b+4)*(b-2)=0
b=4 or b=-2
so we have two sets of answers
4 and 2
and
-2 and -4
I liked the other tutor's logical approach but it left out the negative numbers.

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