Solving cubic equations by completing the cube and higher degree equations by completing powers

Hua-Lin Huang; Shengyuan Ruan; Xiaodan Xu; Yu Ye

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Solving cubic equations by completing the cube and higher degree equations by completing powers

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arxiv 2301.07375 v3 pith:K3ZD3MZ3 submitted 2023-01-18 math.NT math.RA

Hua-Lin Huang , Shengyuan Ruan , Xiaodan Xu , Yu Ye This is my paper · ORCID

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keywords equationscompletingdegreehigherpowersalgebraiccubecubic

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We derive the Cardano formula of cubic equations by completing the cube, and provide radical solutions to some algebraic equations of higher degree by completing powers. The main idea of completing powers arises from Harrison's center theory of higher degree forms. A very simple criterion for such algebraic equations is presented, and the computation amounts to solving linear equations and quadratic equations.

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