SOLUTION: The sum of two numbers is 18. The sum of their squares is at most 170. Find all integral pairs of the numbers that satisfy these conditions.

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Question 1038791: The sum of two numbers is 18. The sum of their squares is at most 170. Find all integral pairs of the numbers that satisfy these conditions.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.X%2BY=18
2.X%5E2%2BY%5E2%3C=170
From 1,
Y=18-X
Substituting into 2,
X%5E2%2B%2818-X%29%5E2%3C=170
X%5E2%2BX%5E2-36X%2B324%3C=170
2X%5E2-36X%2B154%3C=0
X%5E2-18X%2B77%3C=0
%28X%5E2-18X%2B81%29%2B77-81%3C=0
%28X-9%29%5E2-4%3C=0
%28X-9%29%5E2%3C=4
X-9%3C=2 and X-9%3E=-2
X%3C=11 and X%3E=7
7%3C=X%3C=11
So then the integral pairs are,
(7,11)
(8,10)
(9,9)
(10,8)
(11,7)