SOLUTION: Three consecutive even integers are such that the product of the first twois 6 less than 9 time the third. Find the integers.

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Question 240426: Three consecutive even integers are such that the product of the first twois 6 less than 9 time the third. Find the integers.
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
LET X, X+2 & X+4 BE THE 3 CONSECUTIVE INTEGERS.
X(X+2)=9(X+4)-6
X^2+2X=9X+36-6
X^2+2X-9X-36+6=0
X^2-7X-30=0
(X-10)(X+3)=0
X-10=0
X=10 ANS. FOR THE SMALLER INTEGER.
10+2=12 ANS. FOR THE MIDDLE INTEGER.
10+4=14 ANS. FOR THE LARGEST INTEGER.
PROOF:
10*12=9*14-6
120=126-6
120=120
X+3=0
X=-3 ANS. FOR THE SMALLEST INTEGER.
-3+2=-1 ANS. FOR THE MIDDLE INTEGER.
-3+4=1 ANS. FOR THE LARGEST INTEGER.
PROOF:
-3*-1=9*1-6
3=9-6
3=3