Question

The difference of the squares of two positive consecutive even integers is 12 . Find the integers. Use the fact that, if x represents an even integer, than x+2 represents the next consecutive even integer.Please help me solve

Answer 1

Using the fact that, if x represents an even integer, the

`x+2,`

represents the next consecutive even integer, we can set the following equation:

`(x+2)^2-x^2=12.`

Simplifying the above equation, we get:

`x^2+4x+4-x^2=12.`

Adding like terms:

`4x+4=12.`

Subtracting 4 from both sides of the equation we get:

`4x=8.`

Dividing by 4, we get:

`x=2.`

Answer:

`2\text{ and 4.}`