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根据不等式的结构特征,挖掘其蕴含的内在意义,利用圆锥曲线知识,不但能优化解一些不等式的过程,而且还可以提高学生的思维能力.一、利用椭圆知识,巧解一类含绝对值的不等式例1解不等式:|x-2|+|x+2|≥5.分析该不等式含有两个绝对值符号,表示x轴上的点(x,0)到两定点(-2,0)和(2,0)的距离之和大于或等于5.解这类不等式,我们可以先根据椭圆的定义,找到对应椭圆的焦点,再利用椭圆在x轴上的端点的横坐标求解.
According to the structural characteristics of inequality, mining the intrinsic meaning of its implication, using the knowledge of conic curves, not only can optimize the process of solving some inequalities, but also improve the students’ thinking ability.One, using elliptical knowledge, cleverly solve a class of absolute value Inequality Example 1 Solving the inequality: | x-2 | + | x + 2 | ≥5. Analysis The inequality contains two symbols of absolute sign representing the point (x, 0) on the x- And (2,0) is greater than or equal to 5. Solving this type of inequality we can first find the focal point of the corresponding ellipse based on the definition of the ellipse, and then use the abscissa of the end point of the ellipse on the x-axis.