SOLUTION: the product of two consecutive odd intergers is 15. Find all pairs of intergers that satisfy this condition?

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Question 809598: the product of two consecutive odd intergers is 15. Find all pairs of intergers that satisfy this condition?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The consecutive odd integers are 2n%2B1 and 2n%2B3.

%282n%2B1%29%282n%2B3%29=15
4n%5E2%2B2n%2B6n%2B3=15
4n%5E2%2B8n=12
n%5E2%2B2n=3
n%5E2%2B2n-3=0
%28n%2B3%29%28n-1%29=0
'
n=-3 or n=1

Putting these into the general expressions,
the two numbers are -5 and -3
OR
3 and 5.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

the product of two consecutive odd intergers is 15. Find all pairs of intergers that satisfy this condition?

Let smaller of 2 integers be S

Then larger = S + 2

Therefore, S(S + 2) = 15

S%5E2+%2B+2S+=+15

S%5E2+%2B+2S+-+15+=+0

Solve for S. Integers should be {3, 5}, and {- 5, - 3}

You can do the check!!

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