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借助于几何图象对解有关含参数的代数问题(比如方程根的讨论、求解不等式及某些求极值问题的讨论。既直观而又便于校正纯代数解法。这对培养学生全面分析考虑问题进行解题的能力是有利的。下面举例说明其作用。例1。试确定m的实数值,讨论方程(x-5)~(1/2)=mx+2的根的情况。这是本刊1983年第四期P.14例2,原文利用判别式给出了正确的解法。但过程比较繁,且容易遗漏可能出现的各种情况(这一点原文已指
Using geometrical image pairs to solve algebraic problems involving parameters (such as the discussion of equation roots, solving inequalities, and some discussion of extremum problems. It is intuitive and easy to correct for pure algebraic solutions. This will help students develop a comprehensive analysis of the problem. The ability to solve the problem is advantageous, and the following examples illustrate its role: Example 1. Try to determine the real value of m and discuss the case of the root of the equation (x-5) ~ (1/2) = mx + 2. This is the In the fourth issue of P.14, 1983, the original text used the discriminant formula to give the correct solution, but the process was relatively complicated and it was easy to omit all kinds of situations that may occur.