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最值问题是中学数学教学中常见的问题。常用的解题思路有:利用二次函数、利用判别式、利用不等式、利用配方、利用三角函数等。近几年在选择、填空题目中也频频出现,且题目花样新颍,灵活多变,所以学生往往解不出,认为难度较大。本文就最值问题常用方法的灵活应用及一些技巧做一探讨。一形数结合求最值例1 设x、y都是正数,且3x~2+2y~2=6x,问x取得何值时x~2+y~2达到最大值、最小值。并求出这个最大值、最小值。解法一如图1,由于方程3x~2+2y~2=6x表示椭圆。(x-1)~2+y~2/3/2=1,中心为(1,0),
The question of the highest value is a common problem in the teaching of middle school mathematics. The commonly used problem-solving ideas are: using quadratic functions, using discriminants, using inequalities, using recipes, and using trigonometric functions. In recent years, there have been many problems in selecting and filling in blank topics. The new tricks and tricks are flexible and changeable. Therefore, students are often unable to solve problems and think it is more difficult. This article discusses the flexible application of some of the most commonly used methods and some techniques. A number of combinations to find the best example 1 Let x and y be positive numbers and 3x~2+2y~2=6x. When x gets the value, x~2+y~2 reaches the maximum and minimum values. And find the maximum and minimum values. The solution one is shown in Fig. 1, because the equation 3x~2+2y~2=6x represents the ellipse. (x-1)~2+y~2/3/2=1, centered at (1,0),