SOLUTION: sum of the squares of three consecutive odd numbers is 2531.find the numbers.

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Question 470223: sum of the squares of three consecutive odd numbers is 2531.find the numbers.
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
Let x is the odd number, next odd number is %28x%2B2%29, odd number before x is %28x-2%29.
The sum of the squares of three consecutive odd numbers is %28x-2%29%5E2%2Bx%5E2%2B%28x%2B2%29%5E2=2531
Use formula %28a%2B-b%29%5E2=a%5E2%2B-2ab%2Bb%5E2
x%5E2-4x%2B4%2Bx%5E2%2Bx%5E2%2B4x%2B4=2531
3x%5E2=2531-8
3x%5E2=2523
x%5E2=2523%2F3
x%5E2=841
x1=sqrt%28841%29 or x2=-sqrt%28841%29
x1=29 or x2=-29
If x=29 the number
The next odd number is 29%2B2=31, the third odd number is 29-2=27
If x=-29 the number
The next odd number is -29%2B2=-27, the third odd number is -29-2=-31
Answer: (27,29,31) and (-31,-29,-27)