SOLUTION: The process of finding: the product of two consecutive odd integers is 323. What are the integers.

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Question 390818: The process of finding: the product of two consecutive odd integers is 323. What are the integers.
Found 2 solutions by stanbon, richard1234:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The process of finding: the product of two consecutive odd integers is 323. What are the integers.
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1st: 2x-1
2nd: 2x+1
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Equation:
(2x-1)(2x+1) = 323
4x^2-1 = 323
4x^2 = 324
x^2 = 81
x = 9
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1st: 2x-1 = 17
2nd: 2x+1 = 19
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cheers,
Stan H.

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
If you know that they're integers, then write the integers as x and x+2, where x is odd. Then x%28x%2B2%29+=+323. By difference of two squares, x%28x%2B2%29+=+%28x%2B1%29%5E2+-+1, so it follows that %28x%2B1%29%5E2+=+324 --> x+1 = 18 or -18. We conclude that x = 17 or -19 and the two pairs of integers that satisfy are (17, 19) or (-19, -17).