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

Autor:	Huang, Hua-Lin, Ruan, Shengyuan, Xu, Xiaodan, Ye, Yu
Rok vydání:	2023
Předmět:	Mathematics - Number Theory Mathematics - Rings and Algebras 12D10 11E76 15A69
Druh dokumentu:	Working Paper
Popis:	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. Comment: 11 pages. Minor revision. A new version with more details will be published in the American Mathematical Monthly
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2301.07375 Zobrazit plný text záznamu View this record from Arxiv