Question

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

Answer 1

Answer:

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

Step-by-step 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.