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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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