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二次根式求值问题是学习二次根式的难点,学生往往感觉束手无策.其实,如果我们能抓住问题的本质,通过分析,就能找到解题思路.下面举例加以说明.例1当x=3+5(1/2)/2时,求多项式x3-4x2+4x+1的值.分析当学生初次接触此题,首先想到的解题思路是直接代入,但尝试过后便会因计算过程相对繁琐而放弃.有何更好的解题方法呢?这时,教师如果能从二次根式的本质入手引导学生,解题思路就能豁然开朗.
In fact, if we can grasp the nature of the problem, through analysis, we can find the solution to the problem.Example 1 when x = 3 + 5 (1/2) / 2, find the value of the polynomial x3-4x2 + 4x + 1. Analysis When the students first contact with this question, the first thought of solving the problem is the direct substitution, but after trying will be due to the calculation process Relatively cumbersome and give up .How better to solve the problem? At this time, if the teacher can guide the students from the nature of the second root, problem-solving ideas can be bright.