SOLUTION: the sum of the squares of two positive consecutive even integers is 100. Find the integers.

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Question 255742: the sum of the squares of two positive consecutive even integers is 100. Find the integers.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Let X = even integer and x+2 is the next even integer.
(i) x%5E2+%2B+%28x%2B2%29%5E2+=+100
step 1 - expand (i) to get
(ii) x%5E2+%2B+x%5E2+%2B+4x+%2B+4+=+100
step 2 - combine like terms to get
(iii) 2x%5E2+%2B+4x+%2B+4+=+100
step 3 set = 0 and solve by factoring to get
(iv) 2x%5E2+%2B+4x+-+96+=+0
%282x%2B16%29%28x-6%29=0
(2x+16) = 0 - - > x = -8
(x-6) = 0 - - - -> x = 6
since they are positive, we get x = 6 and x+2 = 8.