SOLUTION: The product of two consecutive odd integers is 323. Find the integers. (Hint: If one odd integer is x, the next consecutive odd integer is x + 2. Simplify your answers completely.

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Question 1169474: The product of two consecutive odd integers is 323. Find the integers. (Hint: If one odd integer is x, the next consecutive odd integer is x + 2. Simplify your answers completely. Enter your answers as a comma-separated list.)
The negative integers are ?
.
The positive integers are
. ?
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
x for first odd integer
x+2 for the next odd integer


Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Let x be the EVEN integer exactly midway between the two odd consecutive integers.


Then the odd integers are (x-1) and (x+1), and


    (x+1)*(x-1) = 323.   or


     x^2 - 1    = 323

     x^2        = 323 + 1 = 324

     x                    = +/-  = +/- 18.


So, the positive odd integers are 17 and 19;

    the negative odd integers are -19 and -17.

Solved.

// Solved in a way as it should be done.

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Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
The product of two consecutive odd integers is 323. Find the integers. (Hint: If one odd integer is x, the next consecutive odd integer is x + 2. Simplify your answers completely. Enter your answers as a comma-separated list.)
The negative integers are ?
.
The positive integers are
. ?
As the product is 323, we get: x(x + 2) = 323
Solve that to get the 2 CONSECUTIVE integers!

OR

SIMPLY, take the square root pf 323, which is 17.97220076.
This means that the 1st INTEGER is < 17. Therefore, the 2 CONSECUTIVE INTEGERS are 17 & 19.
They can also be NEGATIVE, or be: - 19 & - 17
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