论文部分内容阅读
化归思想一般是指我们将需要解决的问题,通过某种转化,化归到一类我们已经解决或比较容易解决的问题中去,求得问题的最终有效解答的一种数学思想。在高中数学的教学过程中,利用化归思想求解的例题几乎无处不在,下面举例说明化归思想在高中数学求值中的应用。一、构造函数,化归为函数的性质问题例1已知实数a,b分别满足a~3-3a~2+5a=1,b~3-3b~2+5b=5,则则a+b=__。分析:考虑到两个等式的左侧的表达式一致,可以考虑构造三次函数f(x)=x~3-3x~2+5x,再利用三次函数的性质求解。但是三次函数的性质,高中教材中研究较少,因此可以考虑适当
To return to the general idea is that we will need to solve the problem, through some kind of transformation, to belong to a class we have been resolved or easier to solve the problem, to find the final solution to the problem of a mathematical idea. In high school mathematics teaching process, the use of the idea of the solution to the problem almost everywhere, the following examples illustrate the idea of return to high school mathematics evaluation. First, the constructor, into the nature of the function of the problem Example 1 known real a, b, respectively, to meet a ~ 3-3a ~ 2 + 5a = 1, b ~ 3-3b ~ 2 + 5b = 5, then a + b = __. Analysis: Considering that the expressions on the left side of the two equations are consistent, we can consider constructing the cubic function f (x) = x ~ 3-3x ~ 2 + 5x and then solving the property of cubic function. However, the nature of the cubic function, high school teaching in the study less, so can be considered appropriate