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if (x-1)^2 + (x-2)^2 + (x-3)^2 = 0, then find the solution set for x if x is real
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You can solve this with some geometric reasoning if you consider the plot of each component parabola. Each parabola has a vertex on the x-axis, and you add something to each vertex. This means the given polynomial never touches the x-axis.
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