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If a+b+c=0 and |[a-x,c,b] , [c,b-x,a] , ...

If `a+b+c=0` and `|[a-x,c,b] , [c,b-x,a] , [b,a,c-x]|=0` then prove that either `x=0` or `x=sqrt(3/2(a^2+b^2+c^2))`

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