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Let $$a, b, c$$ be the length of three sides of a triangle satisfying 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 in the interval $$(\alpha, \beta)$$, then $$12(\alpha^2 + \beta^2)$$ is equal to
Correct Answer: 36
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