Posted by **jamie** on Thursday, January 31, 2013 at 6:23pm.

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

- math -
**Reiny**, Thursday, January 31, 2013 at 7:08pm
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

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