SOLUTION: The sum of the squares of two consecutive positive even integers is 340. What are the integers? The answer should be in this form: 6 and 7

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Question 24246: The sum of the squares of two consecutive positive even integers is 340. What are the integers? The answer should be in this form: 6 and 7
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the first positive even integer = x, then the next consecutive positive even integer = (x+2)
x%5E2+%2B+%28x%2B2%29%5E2+=+340 Simplify the left side.
x%5E2+%2B+%28x%5E2+%2B+4x+%2B+4%29+=+340
2x%5E2+%2B+4x+%2B+4+=+340 Subtract 340 from both sides of the equation.
2x%5E2+%2B+4x+-+336+=+0 Factor a 2 from the left side.
2%28x%5E2+%2B+2x+-+168%29+=+0 Factor the parentheses.
2%28x-12%29%28x%2B14%29+=+0 Apply the zero product principle.
%28x-12%29+=+0 and/or %28x%2B14%29+=+0
If x-12+=+0 then x+=+12 This is the first postive even integer.
If x%2B14+=+0 then x+=+-14 Discard this solution as you want positive integers only.

The two integers are: 12 and 14
Check:
12%5E2+%2B+14%5E2+=+144+%2B+196 = 340