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一元二次方程根的判别式是方程中重要的组成部分,也是重要的解题工具.许多数学问题,若纵横联想,挖掘其内在联系,沟通知识之间的关系,妙用判别式进行求解(证),会显得过程简捷、清晰、明快.现举几例,希望能从中得到一些收获.一、比较大小题目1比较(3~(1/2)+2~(1/2)+1)~2与4(3~(1/2)+2~(1/2))的大小.解视(3~(1/2)+2~(1/2)+1)~2-4(3~(1/2)+2~(1/2))为一元二次方程x~2-(3~(1/2)+2~(1/2)+1)x+(2~(1/2)+2~(1/2))=0的根的判别式.容易看出此方程的二根为1,3~(1/2)+2~(1/2).
The discriminant of the root of the quadratic equation is an important component of the equation and is also an important tool for solving problems. Many mathematical problems, if the vertical and horizontal associations, mining their internal relations, the relationship between the communication of knowledge, magical discriminant solution ), Will appear the process is simple, clear, bright .Considering a few examples, hoping to get some gains from it. A comparison of the size of the title 1 comparison (3 ~ (1/2) +2 ~ (1/2) +1) ~ (3 ~ (1/2) + 2 ~ (1/2) +1) ~ 2-4 (3 ~ (1/2) + 2 ~ (1/2) (1/2) + 2 ~ (1/2)) is a quadratic equation x ~ 2- (3 ~ (1/2) + 2 ~ (1/2) +1) x + 2) +2 ~ (1/2)) = 0. It is easy to see that two of the equations are 1, 3 ~ (1/2) + 2 ~ (1/2).