SOLUTION: The difference of 2 possitive integes is 3.& the sum of their square is 89. What are the number????

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Question 1089730: The difference of 2 possitive integes is 3.& the sum of their square is 89.
What are the number????
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Let a be the larger of the two numbers, and b the smaller.
+a+-+b+=+3+ (1)
+a%5E2%2Bb%5E2+=+89+ (2)
(1) —> a = b+3 , substitute this for a in (2):
+%28b%2B3%29%5E2+%2B+b%5E2+=+89+
++%28b%5E2+%2B+6b+%2B+9%29+%2B+b%5E2+=+89+
which will reduce to +%28b-5%29%28b%2B8%29+=+0+
So b=5 (ignore the potential solution b=-8 because b>0)
and a=b+3 = 8
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Ans: +highlight%285%29+ and +highlight%28+8+%29
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Check: +5%5E2+%2B+8%5E2+=+25+%2B+64+=+89+