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Let a,b,c be the lengths of three sides ...

Let `a,b,c` be the lengths of three sides of a triangle satistying the condition `(a^(2)+b^(2))x^(2)-2b(a+c)x+(b^(2)+c^(2))=0` .If the set of all possible values of `x` is the interval `(alpha,beta)` ,then `12(alpha^(2)+beta^(2))` is equal to:

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