SOLUTION: The sum of the squares of two consecutive positive even integers is one hundred sixty-four. Find the two integers.

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Question 416476: The sum of the squares of two consecutive positive even integers is one hundred sixty-four. Find the two integers.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Let x and (x+2) represent the two consecutive 'positive' even integers 

Question states***

 x^2 + (x+2)^2 = 164

Solving for x

 x^2 + x^2 + 4x + 4 = 164

   2x^2 + 4x - 160 = 0

    x^2 + 2x - 80 = 0

factoring

  (x+10)(x-8)= 0  Note:SUM of the inner product(10x) and the outer product(-8x)=2x  

  (x+10)=0  x = -10  Tossing out negative solution for 'positive integer'

  (x-8)= 0  x = 8   the two consecutive 'positive' even integers are 8,10



CHECKING our Answer***

  64 + 100 = 164