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有关含参方程解的问题,一般都转化为函数,利用导数工具,借助数形结合,展开分类讨论.在教学中,学生在遇到如复杂方程a=4x+1(2x-43)?2x有且只有一解,求a的取值范围.学生很容易想到先换元,化繁为简.令t=2x>0,即a=t2+1t2-43t,也会想到利用函数与方程思想,求等式右边对应函数的值域.问题就来了,满足题意吗,等价吗?如何抽丝剥茧,理清头绪,形成正确简单的解题思路?思路一直接法由于方程a=t2+1t2-43t的结构很明确,变量已经分离出来,
The problem of solution of parameters with ginseng equation is usually transformed into function, using the derivative tool, with the help of the combination of number and form, the discussion of classification is carried out.In the teaching, students encounter problems such as complex equation a = 4x + 1 (2x-43) And there is only one solution, the range of a. Students can easily think of the first yuan, simplification. Let t = 2x> 0, that is, a = t2 + 1t2-43t, will also think of the use of functions and equations , The right side of the equation corresponding to the value of the domain. The question came, to meet the ins and outs, the equivalent? How clues, sort out the clues to form the correct and simple problem-solving ideas? The idea has been direct method As the equation a = t2 + 1t2-43t structure is very clear, the variable has been separated,