Hi  

 Let n represent the smallest integer  

n(n+1)(n+2) = n^3- 161

n(n^2 + 3n + 2)= n^3- 161

n^3 + 3n^2 + 2n = n^3 + 161

3n^2 + 2n - 161 = 0

  Integer solution

Integers 7 , 8 , 9

CHECKING our answer***  7*8*9 = 7^3 + 161 = 504

Wish You the Best in your Studies.



 
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation  (in our case ) has the following solutons:

  

  

  

  For these solutions to exist, the discriminant  should not be a negative number.

  

  First, we need to compute the discriminant : .

  

  Discriminant d=1936 is greater than zero. That means that there are two solutions: .

  

    

    

    

    Quadratic expression  can be factored:

  

  Again, the answer is: 7, -7.66666666666667.
Here's your graph:



  

Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!
 

Find three consecutive integers whose product is 161 larger than the cube of the smallest integer

Let the first integer be F

Then other 2 are: F + 1, and F + 2

We then get: 





 ----- Substituting 23F - 21F for 2F

F(3F + 23) - 7(3F + 23) = 0 

F - 7 = 0               OR                    3F + 23 = 0

          OR          3F = - 23 (ignore) 

RELATED QUESTIONS

find three consecutive integers whose product is 85 larger than the cube of the smallest... (answered by stanbon)

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)