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    Constructible Solutions: how to prove x^3−6x+2√(pi) has no constructible solutions?

    Constructible Solutions: how to prove x^3−6x+2√(pi) has no constructible solutions? We know that for cubic polynomial, if there is a constructible root, there is a rational root. But how to prove x^3-6x+2\sqrt{\pi} has no constructible solutions? Any help is really appreciated.
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