Question 299771
The product of two consecutive positive odd integers is one less than twice their sum.
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Note: Odd integers are always one less than
or one more than an even integer.
Even integers are always a multiple of 2.
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Your Problem:
1st: 2x-1
2nd: 2x+1
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Equation:
product = 2(sum) - 1
(2x-1)(2x+1) = 2(2x-1+2x+1)-1
4x^2-1 = 2(4x) -1
4x^2 = 8x
4x(x-2) = 0
x = 0 or x = 2
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If x = 0:
1st = 2x-1 = -1
2nd = 2x+1 = 1
Since you want "positive odd integers", x = 0 is not a solution.
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If x = 2:
1st = 2x-1 = 3
2nd = 2x+1 = 5
This pair is the only solution.

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Cheers,
Stan H.