SOLUTION: The difference of two positive numbers is 5 and the sum of their squares is 233. What are the numbers?

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Question 698631: The difference of two positive numbers is 5 and the sum of their squares is 233. What are the numbers?
Answer by checkley79(3341) About Me  (Show Source):
You can put this solution on YOUR website!
X-Y=5
X=5+Y
X^2+Y^2=233
(5+Y)^2+Y^2=233
25+10Y+Y^2+Y^2-233=0
2Y^2+10Y-208=0
2(Y^2+5Y-104)=0
2(Y+13)(Y-8)=0
Y-8=0
Y=8 ANS. FOR THE SMALLER NUMBER.
X-8=5
X=5+8=13 ANS. FOR THE LARGER NUMBER.
PROOF:
13^2+8^2=233
169+64=233
233=233