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《数学教学研究》1984年第1期中马振民同志《关于根式(m+n~(1/2))~(1/2)的化简》的文章(其中m,n为整数(实为正整数),n为不完全平方数。化简指能否化为A~(1/2)±B~(1/2)的形式。其中A、B为正有理数)。证明了一个定理,即形如(m±n~(1/2))~(1/2)的根式能化为A~(1/2)±B~(1/2)的充要条件为m~2-n为一完全平方数。的确为此类根式的化简提供了一个判别准则和化简的一般方法。阅后很受启发。为了做到深知浅出、推而广之,本文也想谈谈此类根式的化简。形如(m±n~(1/2))~(1/2)的根式通常称为复合二
Mathematical Teaching Research, No. 1, 1984, China Comrade Ma Zhenmin’s article on the simplification of the root formula (m+n~1/2)~(1/2) (where m and n are integers (actually positive integers) ), n is the incomplete square. Simplified means can be converted into A ~ (1/2) ± B ~ (1/2) form, where A, B is a positive rational number). A theorem is proved that the necessary and sufficient condition for the form of (m±n~(1/2))~(1/2) to be A(1/2)±B(1/2) is m~2-n is a complete square number. It does provide a discriminatory criterion and a general method of simplification for such rooted simplification. After reading it was inspired. In order to be well-informed and promoted, this article also wants to talk about the simplification of such radicals. The form of (m±n~(1/2))~(1/2) is often called compound two.