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HMMT November 2019 U18

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The polynomial x3−3x2+1x^{3}-3 x^{2}+1 has three real roots r1,r2r_{1}, r_{2}, and r3r_{3}. Compute

3r1−23+3r2−23+3r3−23\sqrt[3]{3 r_{1}-2}+\sqrt[3]{3 r_{2}-2}+\sqrt[3]{3 r_{3}-2}

Dataset text NuminaMath olympiads. Quoted with source.

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