SOLUTION: find two consecutive odd numbers whose product is 255

Question 125012: find two consecutive odd numbers whose product is 255
Found 3 solutions by josmiceli, jim_thompson5910, dolly:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
If is odd, is the next odd number

The solutions are

The numbers are 15 and 17
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Consecutive odd integers follow the pattern , , , etc

Since the product of two consecutive odd integers is 255, this means we have the equation

Foil the left side

Subtract 255 from both sides

Factor the left side

Now set each factor equal to zero:
or

or Now solve for x in each case

-----------------

Let's use the first solution to find the first pair of numbers

Now plug in into the first equation

Now plug in into the second equation

So the first pair of numbers are -17 and -15

-------------------

Let's use the second solution to find the second pair of numbers

Now plug in into the first equation

Now plug in into the second equation

So the second pair of numbers are 15 and 17

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Answer:

So the pair of consecutive odd integers that multiply to 255 are

-17 and -15

OR

15 and 17
Answer by dolly(163)   (Show Source): You can put this solution on YOUR website!
Let the two odd numbers be x and x+2
Then x(x+2) = 255
==> x^2 + 2x - 255 = 0
==> x^2 + 17x - 15x - 255 = 0
==> x(x+17)-15(x+17) = 0
==> (x+17)(x-15) = 0
==> x+17 = 0 or x-15 = 0
==> x = -17 or x = 15
So the two odd numbers are 15 and 17.
good luck!!
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