Question

The sum of the squares of two consecutive positive even integers is 340. How do you find the number?

Answer 1

The numbers are `12` and `14`

Explanation:

To find the answer, set up an equation.

Set `x` equal to the lower number, and `x+2` as the higher number since they are consecutive even numbers so they are two apart.

Now write out the equation according to the question

`(x)^2+color(blue)((x+2))^2 = 340`

`x^2 + color(blue)(x^2 + 4x + 4) = 340`

Combine like terms.

`2x^2 + 4x + 4 = 340`

Set equal to zero so you can factor.

`2x^2 + 4x -336 = 0`

`(2x+ 28)(x-12) = 0`

`x= -14, 12`

`x=12` because the answer must be positive according to the question.

That means `x+2` is 14.

You can double check:

`(12)^2 + (14)^2= 340`

`144+196=340`

`340=340`