i need help.

Question

the product of three consecutive integers is equal to their sum. What are the integers

 

Answer 1

n-1, n, and n+1 are the integers

n(n-1)(n+1)=n+n-1+n+1

n(n^2-1)=3n

n^3-n-3n=0

n^3-4n=0

n(n^2-4)=0

n=0

n-1=-1 and n+1=1

-1, 0, and 1 is one solution

n^2-4=0

(n-2)(n+2)=0

n-2=0

n=2

n-1=1 and n+1=3

1, 2, and 3 is another solution

n+2=0

n=-2

n-1=-3 and n+1=-1

-3, -2, and -1 is the third solution