Solving cubic equations by completing the cube and higher degree equations by completing powers
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914712114954240 |
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| author | Huang, Hua-Lin Ruan, Shengyuan Xu, Xiaodan Ye, Yu |
| author_facet | Huang, Hua-Lin Ruan, Shengyuan Xu, Xiaodan Ye, Yu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_07375 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solving cubic equations by completing the cube and higher degree equations by completing powers Huang, Hua-Lin Ruan, Shengyuan Xu, Xiaodan Ye, Yu Number Theory Rings and Algebras 12D10, 11E76, 15A69 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. |
| title | Solving cubic equations by completing the cube and higher degree equations by completing powers |
| topic | Number Theory Rings and Algebras 12D10, 11E76, 15A69 |
| url | https://arxiv.org/abs/2301.07375 |