Question

the product of three consecutive integers is 22 less than the cube of the middle integer. Find the integer.

Answer 1

let the 3 consecutive integers be
x-1, x, and x+1

( I wanted to cube x , not x+1 )

x(x-1)(x+1) = x^3 - 22
x^3 - x = x^3 - 22
x = 22

the 3 integers are 21 , 22, and 23

check: product of 3 numbers = 21x22x23 = 10626
cube of 22 = 10648
is the product 22 less than the cube? YES