SOLUTION: Find 3 consecutive odd integers such that the product of the first and third integers is 4 less than the square of the second integer.

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Question 164036: Find 3 consecutive odd integers such that the product of the first and third integers is 4 less than the square of the second integer.


Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
Let:
the first odd integer = x
the second odd integer = x + 2
the third odd integer = x + 4
x%2A%28x+%2B+4%29+=+%28x+%2B+2%29%5E2+-+4
<=> x%5E2+%2B+4x+=+x%5E2+%2B+4x+%2B+4+-+4
<=> x%5E2+%2B+4x+-+x%5E2+-+4x+=+4+-+4
<=> 0+=+0
from the result above, we can conclude that every 3 consecutive odd integers has such characteristic (the product of the first and third integers is 4 less than the square of the second integer)
1%2A5+=+3%5E2+-+4
3%2A7+=+5%5E2+-+4
5%2A9+=+7%5E2+-+4
and so on.