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当方程或不等式中含有字母参数时,学生常习惯于用参数去表示、刻划主元,但对于如何确定参数的范围,却普遍感到棘手,而这类问题的实质是,参数与主元既互相牵制,又互相依赖.通过恰当地变形,明确参数与主元的依存关系,对我们正确、合理地解决参数范围问题,有着普遍的指导意义。 1.直接依赖“主元”(当问题中主元的值、范围及其它属性暴露清晰或易于利用时)。 例1 已知方程组的解满足x<0,y>0.求实数k的取值范围。 分析:由于题目中的两个主元x、y的范围已明确
When the equations or inequalities contain alphabetic parameters, students are often used to represent and characterize the pivotal elements with parameters, but it is generally difficult to determine the range of parameters, and the essence of such problems is that both the parameters and the pivotal elements To check each other and rely on each other. Through appropriate deformation, the clear dependence of the parameters and principal elements has a universal guiding significance for us to correctly and reasonably solve the parameter range problem. 1. Directly rely on the “principal element” (when the value, scope, and other attributes of the subject in the question are exposed or easy to use). Example 1 The solution of the known system of equations satisfies x<0, y>0. Find the range of real numbers k. Analysis: Since the two principal elements x, y in the title have been defined