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

Apr 10, 2018

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

${\left(x\right)}^{2} + {\textcolor{b l u e}{\left(x + 2\right)}}^{2} = 340$

${x}^{2} + \textcolor{b l u e}{{x}^{2} + 4 x + 4} = 340$

Combine like terms.

$2 {x}^{2} + 4 x + 4 = 340$

Set equal to zero so you can factor.

$2 {x}^{2} + 4 x - 336 = 0$

$\left(2 x + 28\right) \left(x - 12\right) = 0$

$x = - 14 , 12$

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

That means $x + 2$ is 14.

You can double check:

${\left(12\right)}^{2} + {\left(14\right)}^{2} = 340$

$144 + 196 = 340$

$340 = 340$