SOLUTION: My question: The sum of the squares of two consecutive positive intergers is 85; Find the intergers.

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Question 15287:
My question: The sum of the squares of two consecutive positive intergers is 85; Find the intergers.

Answer by wgunther(43) About Me  (Show Source):
You can put this solution on YOUR website!
let x equal the lower positive integer
x%5E2+%2B+%28x%2B1%29%5E2+=+85
x%5E2+%2B+x%5E2+%2B+2x+%2B+1+=+85
2x%5E2+%2B+2x+-+84+=+0
x%5E2+%2B+x+-+42+=+0
%28x%2B7%29%28x-6%29=0
so x = {-7, 6}, which makes sense, because when you square a negative you get a positive. But your question is consecutive POSITIVE integers, hence the answer is 6 and 7.