SOLUTION: If the difference between two numbers is 5, and the difference between the squares of those numbers is also 5, how can I find out what the two numbers are using an algebraic method

Question 821559: If the difference between two numbers is 5, and the difference between the squares of those numbers is also 5, how can I find out what the two numbers are using an algebraic method (not trial and error)?
I have found out one pair of numbers that have the required criteria, (3 and -2), but this was through trial and error.

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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y - x = 5
y = x + 5
yy - xx = 5
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yy - xx = 5
(x + 5)(x + 5) - xx = 5
xx + 10x + 25 - xx = 5
10x + 25 = 5
10x = -20
x = -2
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answer:
x = -2
y = 3
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