SOLUTION: there are three consecutive odd integers. if we take the difference of the third and the first integers, it becomes equal to the product of the first and second integers plus the s

Algebra.Com
Question 885592: there are three consecutive odd integers. if we take the difference of the third and the first integers, it becomes equal to the product of the first and second integers plus the square of the second integer. what is the third odd integer?
hint: x be the first integer
x+2 be the second odd integer
x+4 be the third odd integer
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
List of the three consecutive odd integers:
2x+1
2x+3
2x+5.

Difference between first and third: .

Product of first and second, plus square of the second:

They are given as equal:


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I see now your hint of "let x be the first integer"; but I followed a more typical method. I used x as any positive whole integer, and then built the consecutive ODD integers based on this idea. 2x will be an EVEN number, but 2x plus an ODD number will be an ODD number.
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Now, when you solve for x, this will not be your first integer of the list. Your first integer of the list will be .
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
there are three consecutive odd integers. if we take the difference of the third and the first integers, it becomes equal to the product of the first and second integers plus the square of the second integer. what is the third odd integer?
hint: x be the first integer
x+2 be the second odd integer
x+4 be the third odd integer


Since x is the 1st integer, then 2nd = x + 2, and 3rd = x + 4

Therefore, 





2x(x + 3) = 0



x + 3 = 0                OR          2x = 0

x = - 3                  OR          x = 0 (ignore)



Third ODD integer: - 3 + 4, or  

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