SOLUTION: MATH QUESTION~ please help! Find three positive consecutive numbers such that the square of the sum exceeds the sum of their squares by 214. I know the number can be x and t

Question 761066: MATH QUESTION~
please help!
Find three positive consecutive numbers such that the square of the sum exceeds the sum of their squares by 214.
I know the number can be x and then the two other numbers can be x-1 and x+1... x being the middle number.
Thank You
:D
Answer by ramkikk66(644) (Show Source): You can put this solution on YOUR website!
You started right :)
If the 3 numbers are x-1, x and x+1,
their sum is
Square of the sum =
Sum of the squares =
From the problem statement

Simplifying and move all x^2 terms to Left side, we get

---> Since it is given that the numbers are positive
The 3 numbers are 5,6 and 7
:)
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