SOLUTION: Find three consecutive positive odd integers such that the sum of their squares is 371.

Question 1154151: Find three consecutive positive odd integers such that the sum of their squares is 371.
Found 3 solutions by ramkikk66, mananth, Alan3354:
Answer by ramkikk66(644)   (Show Source): You can put this solution on YOUR website!
Let the 3 odd integers be x - 2, x and x + 2
Square of the 1st =
Square of the 2nd =
Square of the 3rd =
Adding the 3 equations above, and equating to the given sum, we get

So
since it is given that x is positive, it cannot be -11
So the 3 numbers are , and .
Check by adding the 3 squares
. Checked!
Ans: 9, 11, 13
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Find three consecutive positive odd integers such that the sum of their squares is 371.
let n be the first positive odd integer
second will be n+2
Third will be n+4
n^2 +(n+2)^2 +(n+4)^2=371
n^2 +n^2 +4n +4 + n^2 +8n +16=371
3n^2+12n + 20=371
3n^2+12n-351=0
divide by 3
n^2+4n-117=0
(n+13)(n-9)=0
n=-13 Or n=9
but n is positive
Therefore n=9
The numbers are 9,11,13
CHECK
9^2+11^2+13^2=371

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Find three consecutive positive odd integers such that the sum of their squares is 371.
-----------
371/3 = 123.666...
The nearest square is 121 = 11^2
---> 11 is the middle integer

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