The sum of the squeres of two consecutive positive even numbers is 340. Find the numbers

The numbers are 12 and 14 ONLY

Step-by-step 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

+

(

x

+

2

)

2

=

340

x

2

+

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

(

2

x

+

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