SOLUTION: Find three consecutive even integers such that the sum of the squares of the first and second integers is equal to twice the third integers. Find the integers.

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Question 992383: Find three consecutive even integers such that the sum of the squares of the first and second integers is equal to twice the third integers. Find the integers.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the consecutive even integers =
+n+, +n%2B2+, and +n+%2B+4+
given:
+n%5E2+%2B+%28+n%2B2+%29%5E2+=+2%2A%28+n%2B4+%29+
+n%5E2+%2B+n%5E2+%2B+4n+%2B+4+=+2n+%2B+8+
+2n%5E2+%2B+2n-+4+=+0+
+n%5E2+%2B+n+-+2+=+0+
+%28+n+%2B+2+%29%2A%28+n+-+1+%29+=+0+
+n+=+-2+ ( ignore the positive root )
+n+%2B+2+=+0+
+n+%2B+4+=+2+
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The consecutive even integers are:
-2, 0, and 2
------------
check:
+n%5E2+%2B+%28+n%2B2+%29%5E2+=+2%2A%28+n%2B4+%29+
+%28-2%29%5E2+%2B+%28+-2%2B2+%29%5E2+=+2%2A%28+-2%2B4+%29+
+4+%2B+0+=+2%2A2+
+4+=+4+
OK