SOLUTION: Find two consecutive positive odd numbers given that difference between their reciprocals is 2\63

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Question 508462: Find two consecutive positive odd numbers given that difference between their reciprocals is 2\63
Answer by Alan3354(69443) About Me  (Show Source):
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Find two consecutive positive odd numbers given that difference between their reciprocals is 2\63
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Just eyeing the numbers, I'd guess 7 & 9.
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1%2Fx+-+1%2F%28x%2B2%29+=+2%2F63
Multiply thru by x(x+2)
%28x%2B2%29+-+x+=+%282x%5E2+%2B+4x%29%2F63
2%2A63+=+2x%5E2+%2B+4x
x%5E2+%2B+2x+-+63+=+0
(x+9)*(x-7) = 0
x = 7 --> 7 & 9
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x = -9 --> -9 & -7