SOLUTION: The sum of the squares of three consecutive integers is 50. Find these integers.

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Question 1066767: The sum of the squares of three consecutive integers is 50. Find these integers.
Found 2 solutions by josgarithmetic, Alan3354:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B%28x%2B1%29%5E2%2B%28x%2B2%29%5E2=50, if the first integer is x.

x%5E2%2Bx%5E2%2B2x%2B1%2Bx%5E2%2B4x%2B4=50
3x%5E2%2B6x%2B5=50
3x%5E2%2B6x-45=0
x%5E2%2B2x-15=0

%28x%2B5%29%28x-3%29=0

Either x=-5 or x=3. See which of them works, or if both work.

3%5E3%2B4%5E2%2B5%5E2=50?
9%2B16%2B25
25%2B25
50=50
-
%28-5%29%5E2%2B%28-4%29%5E2%2B%28-3%29%5E2
25%2B16%2B9
same.
50

--------------------------------------
ANSWER: Either -5, -4, -3
OR
3, 4, 5
-------------------------------------

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the squares of three consecutive integers is 50. Find these integers.
===============
50/3 =~ 16
sqrt(16) = 4
--> 3, 4 & 5 or -5, -4 & -3