SOLUTION: the product of two consecutive positive integers is greter than twice the next integer by 8. what are the three integers?

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Question 445152: the product of two consecutive positive integers is greter than twice the next integer by 8. what are the three integers?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Consecutive integers are integers that follow each other in order, like 1,2,3....
represent the first set with n, second one with n+%2B+1, third one n+%2B+2
given:
n%28n+%2B+1%29=2%28n+%2B+2%29%2B8
n%5E2+%2B+n=2n+%2B+4%2B8
n%5E2+%2B+n+-2n+-+12=0
n%5E2+-n+-+12=0...solve quadratic for n
n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
n+=+%28-%28-1%29+%2B-+sqrt%28%28-1%29%5E2-4%2A1%2A%28-12%29+%29%29%2F%282%2A1%29+
n+=+%281+%2B-+sqrt%281%2B48+%29%29%2F2+
n+=+%281+%2B-+sqrt%2849%29%29%2F2+
n+=+%281+%2B-+7%29%2F2+
n+=+%281+%2B+7%29%2F2+
n+=+8%2F2+
n+=+4...or

n+=+%281+-+7%29%2F2+
n+=+-6%2F2+
n+=+-3.....now find sets of numbers
let's go with n+=+4
n=4, second one with n+%2B+1=5, third one n+%2B+2=6
first set of numbers is: 4,5,6
now go with n+=+-3

n=-3, second one with n+%2B+1=-2, third one n+%2B+2=-1

the second set of numbers is: -3, -2, -1

check both:
n%28n+%2B+1%29=2%28n+%2B+2%29%2B8....plug in 4,5,6
4%285%29=2%286%29%2B8
20=12%2B8
20=20
n%28n+%2B+1%29=2%28n+%2B+2%29%2B8....plug in -3,-2,-1
-3%28-2%29=2%28-1%29%2B8
6=-2%2B8
6=6