论文部分内容阅读
数学习题都包含已知条件和所求结论两部分,有些题目的条件或结论常存在特殊性,在解题时,注意到这一点,常可找到解题捷径。例1 解方程3/(x+4)/(1-x~2)~(1/2)=10 分析此为分式无理方程,若去分母化为有理方程来解,不仅计算很繁,而且还会出现高次方程。如能抓住已知条件中的两个分母和它们之间关系的特殊性,即(1-x~2)~(1/2)有意义,故|x|≤1,且x~2+((1-x)~(1/2))~2=1,自然会想到|sinα|≤1
The number of learning questions contains both known conditions and the required conclusions. The conditions or conclusions of some topics often have particularities. When solving problems, it is important to note the shortcomings. Example 1 Solution Equation 3/(x+4)/(1-x~2)~(1/2)=10 Analysis This is a fractional irrational equation. If the de-mineralization is solved as a rational equation, it is not only very complicated to calculate. And there will be higher order equations. If we can grasp the particularity of the two denominators in the known conditions and the relationship between them, that is, (1-x~2)~(1/2) makes sense, so |x|≤1, and x~2+ ((1-x) ~ (1/2)) ~ 2 = 1, naturally think of |sinα|≤1