Question

When three consecutive positive integers are multiplied, the product is 16 times the sum of the three integers. What is the difference of the product minus the sum?

Answer 1

We have the following:

Let the 3 consecutive positive integers be:

`\begin{gathered} x \\ x+1 \\ x+2 \end{gathered}`

The product is:

`x\cdot(x+1)\cdot(x+2)`

The sum is:

`x+x+1+x+2=3x+3`

We're told the product is equivalent to:

`\begin{gathered} x\cdot(x+1)\cdot(x+2)=16\cdot(3x+3) \\ x\cdot(x+1)\cdot(x+2)=16\cdot3(x+1) \\ x\cdot(x+2)=48 \\ x^2+2x=48 \\ x^2+2x-48=0 \end{gathered}`

Now subtract the sum from the product:

`\begin{gathered} x^2+2x-48-3x-3 \\ x^2-x-51 \end{gathered}`