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方程是一种重要的数学模型,也是一种重要的数学思想.在初中数学竞赛中,含字母系数的方程及高次方程的应用与拓展始终是学生学习上的热点与难点.解决此类问题,常常涉及分类讨论、数形结合等数学思想,用到因式分解、整除和不定方程的解法等有关知识,具有较强的综合性和技巧性.现选竞赛试题为例,谈谈此类方程在竞赛中的拓展应用.
The equation is an important mathematical model and also an important mathematical idea.In the junior middle school mathematics competition, the equation with alphanumerical coefficients and the application and development of the high-order equation are always the hot spots and difficulties in the students’ learning. , Often involving classification discussion, mathematical combination of numbers and other mathematical ideas, the use of factorization, divisibility and indefinite equation solutions and other related knowledge, with strong synthesis and skills. Expansion and Application of Equations in Competition.