SOLUTION: find three consecutive integers whose product is 85 larger than the cube of the smallest integer

Question 811157: find three consecutive integers whose product is 85 larger than the cube of the smallest integer
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find three consecutive integers whose product is 85 larger than the cube of the smallest integer
----------
1st: x-1
2nd: x
3rd: x+1
------------
Equation:
x(x^2-1) = (x-1)^3 + 85
-----
x^3 - x = x^3-3x^2+3x+84
-------
3x^2-4x-84 = 0
(x-6)(3x+14) = 0
-------
Positive solution::
x = 6
==================
1st: x-1 = 5
2nd: x = 6
3rd: x+1 = 7
=================
Cheers,
Stan H.
=================
RELATED QUESTIONS
Find three consecutive integers whose product is 161 larger than the cube of the smallest (answered by ewatrrr,MathTherapy)

find three consecutive integers whose product is 56 larger than the cube of the smallest... (answered by CubeyThePenguin)

Find three consecutive integers whose product is 208 larger that the cube of the smallest (answered by CubeyThePenguin)

Find three consecutive integers whos product is 120 larger than the cube of the smallest... (answered by solver91311)

The product of three consecutive integers is 21 more than the cube of the smallest... (answered by DrBeeee,algebrahouse.com)

Can you find three consecutive integers whose product is 5 greater than the cube of the... (answered by Theo)

The product of three consecutive odd integers is ten less than the cube of the smallest... (answered by josgarithmetic)

The product of three consecutive integers is 21 more than the cube of the smallest... (answered by greenestamps,Alan3354)

The product of three consecutive integers is 21 more than the cube of the smallest... (answered by math_helper)