SOLUTION: find two consecutive odd numbers whose product is 255

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Question 125012: find two consecutive odd numbers whose product is 255
Found 3 solutions by josmiceli, jim_thompson5910, dolly:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If n is odd, n%2B2 is the next odd number
n%28n+%2B+2%29+=+255
n%5E2+%2B+2n+-+255+=+0
%28n+%2B+17%29%28n+-+15%29
The solutions are
n+=+-17
n+=+15
n+%2B+2+=+17
The numbers are 15 and 17

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Consecutive odd integers follow the pattern 2x%2B1, 2x%2B3, 2x%2B5, etc




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

%282x%2B1%29%282x%2B3%29=255


4x%5E2%2B8x%2B3=255 Foil the left side


4x%5E2%2B8x-252 Subtract 255 from both sides


4%28x%2B9%29%28x-7%29=0 Factor the left side



Now set each factor equal to zero:
x%2B9=0 or x-7=0

x=-9 or x=7 Now solve for x in each case


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Let's use the first solution x=-9 to find the first pair of numbers

Now plug in x=-9 into the first equation 2x%2B1

2%28-9%29%2B1=-18%2B1=-17

Now plug in x=-9 into the second equation 2x%2B3

2%28-9%29%2B3=-18%2B3=-15


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

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Let's use the second solution x=7 to find the second pair of numbers

Now plug in x=7 into the first equation 2x%2B1

2%287%29%2B1=14%2B1=15

Now plug in x=7 into the second equation 2x%2B3

2%287%29%2B3=14%2B3=17


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) About Me  (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!!