SOLUTION: When the product of three consecutive integers is decreased by the cube of the smallest, the result is 85. What are the integers?

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: When the product of three consecutive integers is decreased by the cube of the smallest, the result is 85. What are the integers?      Log On


   

Question 1010201: When the product of three consecutive integers is
decreased by the cube of the smallest, the result is 85.
What are the integers?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x, x+1,x+2 are the integers
Their product is( x^2+3x+2)*x=
x^3+3x^2+2x
subtract x^3
have 3x^2+2x=85
3x^2+2x-85=0
(3x+17)(x-5)=0
x=5 only integer solution.
5,6,7 are the numbers
Their product is 210
decreased by 5^3 or 125, and that is 85.