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If A(x(1), y(1)), B(x(2), y(2)), and, C(...

If `A(x_(1), y_(1)), B(x_(2), y_(2))`, and, `C(x_(3), y_(3))` are vertices of an equilateral triangle whose each side is equal to a, then prove that `|(x_(1), y_(1), 2),(x_(2), y_(2), 2),(x_(3), y_(3), 2)|^(2) = 3a^(4)`.

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