SOLUTION: The product of two consecutive positive odd integers is one less than three times their sum. Find the integers. can someone show me how to set this up im so confused

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Question 325142: The product of two consecutive positive odd integers is one less than three times their sum. Find the integers.
can someone show me how to set this up im so confused
Found 2 solutions by scott8148, checkley77:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
consecutive odd integers are two units apart (3 and 5 , 11 and 13 , etc.)

n(n+2) + 1 = 3(n + n + 2)

n^2 + 2n + 1 = 6n + 6

n^2 - 4n - 5 = 0

(n - 5)(n + 1) = 0

n = 5 , n+2 = 7

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
X & X+2 ARE THE 2 CONSECUTIVE INTEGERS.
X(X+2)=3(X+X+2)-1
X^2+2X=3(2X+2)-1
X^2+2X=6X+6-1
X^2+2X-6X-5=0
X^2-4X-5=0
(X-5)(X+1)=0
X-5=0
X=5 ANS.
5+2=7 ANS.
X+1=0
X=-1 ANS.
-1+2=1 ANS.
PROOF:
5*7=3(5+7)-1
35=3*12-1
35=36-1
35=35