If three numbers form an arithmetic sequence, their sum is 15 and their sum of squares is 83, what are the three numbers

Let X be in the middle
Then let x-a, x, x + a
(x-a)+x+(x+a)=15
3x=15
x=5
(x-a)²+x²+(x+a)²=83
3x²+2a²=83
2a²=83-75=8
a=±2
So the three numbers are 3,5,7 or 7,5,3

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