SOLUTION: The sum of the squares of three consecutive integers is 110. Find the numbers.

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Question 406783: The sum of the squares of three consecutive integers is 110. Find the numbers.
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi

three consecutive integers

Let x,(x+1),(x+2) represent the three consecutive integers

Question states***

x^2 +(x+1)^2+(x+2)^2 = 110

Solving for x

 3x^2 + 6x  + 5 = 110

 3x^2 + 6x  -105 = 0

 3(x^2 + 2x - 35)  = 0

  (x^2 + 2x - 35)  = 0 

factoring

  (x+7)(x-5) = 0 Note:SUM of the inner product(7x) and the outer product(-5x) = 2x

  (x+7)=0  |x = -7  The three consecutive integers are -5,-6,-7

  (x-5)=0  |x = 5   The three consecutive integers are 5,6,7





CHECKING our Answer(s)***

25 + 36 + 49 = 110