SOLUTION: The product of two consecutive odd integers is one less than twice their sum. Find the integers.

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Question 810903: The product of two consecutive odd integers is one less than twice their sum. Find the integers.
Found 2 solutions by mananth, Benyamin:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
x & x+2 are the integers
x(x+2) = x+x+2-1
x^2+2x=2x+1
x^2=1
x=+/-1
1,3
-1,-3

Answer by Benyamin(2) About Me  (Show Source):
You can put this solution on YOUR website!
Two consecutive odd numbers are as 2%2Ak%2B1 and 2%2Ak%2B3. Therefore, the assumption concludes this equation:
%282%2Ak%2B1%29%2A%282%2Ak%2B3%29+=+2%2A%28%282%2Ak%2B1%29%2B%282%2Ak%2B3%29%29-1
simplifying the above equation, we see that:
k=1
and so, the answer is 3 and 5.
Regards