If the roots of the equation (x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0 are equal, prove that a = b = c.

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If the roots of the equation (x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0 are equal, prove that a = b = c.

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