SOLUTION: Solve by using a quadratic equation to find three consecutive integers such that the sum of their squares is 1877.

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Question 416350: Solve by using a quadratic equation to find three consecutive integers such that the sum of their squares is 1877.
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Let the consecutive integers be n, n+1, and n+2
We have n%5E2+%2B+%28n%2B1%29%5E2+%2B%28n%2B2%29%5E2+=+1877
Multiplying terms gives n%5E2+%2B+n%5E2+%2B+2n+%2B+1+%2B+n%5E2+%2B+4n+%2B+4+=+1877
Collecting like terms and putting in the proper form gives
+3n%5E2+%2B+6n+-+1872+=+0+
Applying the quadratic formula we get
n+=+%28-6+%2B-+sqrt%286%5E2+-+4%2A3%2A%28-1872%29+%29%29%2F%282%2A3%29 -> %28-6+%2B-+150%29%2F6
This gives n = -26, 24
So one set of consecutive integers is 24,25,26 and the other is -26,-25,-24