SOLUTION: The sum of the squares of two consecutive positive even integers is 340. Find the integers. Can't for the life of me figure this one out. Please help!! Joanne

Question 110810: The sum of the squares of two consecutive positive even integers is 340. Find the integers.
Can't for the life of me figure this one out. Please help!!
Joanne
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Consecutive even integers follow the form 2x, 2x+2, etc

So the sum of their squares is

Square 2x to get 4x^2

Foil

Subtract 340 from both sides

Subtract 340 from both sides

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=8, b=8, and c=-336

Square 8 to get 64

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 8 to get 16

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Since the values of x are and , this means our two numbers are

,

or

,
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