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

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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) About Me  (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 x-1%2Bx%2Bx%2B1+=+3%2Ax
Square of the sum = 9%2Ax%5E2
Sum of the squares = %28x+-+1%29%5E2+%2B+x%5E2+%2B+%28x+%2B+1%29%5E2+=+3%2Ax%5E2+%2B+2
From the problem statement
9%2Ax%5E2+=+3%2Ax%5E2+%2B+2+%2B+214
Simplifying and move all x^2 terms to Left side, we get
6%2Ax%5E2+=+216
x%5E2+=+36
x+=+6 ---> Since it is given that the numbers are positive
The 3 numbers are 5,6 and 7
:)