方程与曲线论〔17〕——等分方程定理(A_3型)

Equation and curves——theorem of halved-equation(Type A_3)

对任意正整数n ,运用 (A3 型 )等分方程定理的通项公式 ,就可产生复系数的一元n次代数方程的一般式 ,每个一般式又可根据坐标平面上的任意一点产生具体给定方程式 ,再通过每个给定方程的配套求根公式 ,就可准确而简便地求出n个复根。由于n的无限性 ,因此 ,由定理所产生的方程。

When a formula for general term of halved-equation (Type A 3)is applied to an arbitrary positive integer n,a general equation of unary nth algebraic expression,with complex coefficients,can be obtained.Each general equation produces a concrete given equation,according to any point in an coordinate plane.Then n complex roots can be got accurately and easily through its necessary root extracting formula.Equation and extraction of root resulting from the theorem are indefinite,because of the indefinitness of n.