Solving cubic equations by completing the cube and higher degree equations by completing powers
Number Theory
2024-03-14 v3 Rings and Algebras
Abstract
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.
Cite
@article{arxiv.2301.07375,
title = {Solving cubic equations by completing the cube and higher degree equations by completing powers},
author = {Hua-Lin Huang and Shengyuan Ruan and Xiaodan Xu and Yu Ye},
journal= {arXiv preprint arXiv:2301.07375},
year = {2024}
}
Comments
11 pages. Minor revision. A new version with more details will be published in the American Mathematical Monthly