Question

The product of two consecutive even integers is 48. Find the integers

Answer 1

The two consecutive integers are 6 and 8 or -8 and -6.

Explanation:

The product of two consecutive even integers is 48, and we want to find the two integers.

We will let x represent the first even integer.

Then the consecutive even integer will be (x + 2).

Its product is 48. Therefore:

`x(x+2)=48`

Solve for x. Since this is a quadratic, we should get one side to equal to 0. Expand:

`x^2+2x=48`

Subtract 48 from both sides:

`x^2+2x-48=0`

Factor:

`(x+8)(x-6)=0`

Zero Product Property:

`x+8=0\text{ or } x-6=0`

Solve for each case:

`x=-8\text{ or } x=6`

Therefore, our two consecutive integers are 6 and 8 or -8 and -6.