论文部分内容阅读
分类思想是化整为零、分别对待、各个击破的一种思维策略,是数学中的一种重要的思想方法.求解的关键在于正确地进行分类,即选择一个分类标准,对所讨论的对象进行全面分类,确保分类的科学——既不重复,也不遗漏.一、方程问题中的分类讨论例1(2013年荆州)已知:关于x的方程kx~2-(3k-1)x+2(k-1)=0.(1)求证:无论k为何实数,方程总有实数根.(2)若此方程有两个实数根x_1,x_2,且|x_1-x_2|=2,求k的值.
The idea of classification is a kind of thinking method in mathematics, which is a kind of thinking method in mathematics.The key of solving is to classify correctly, that is to choose a classification standard, A comprehensive classification to ensure that the science of classification - neither duplication nor omission. First, the classification of equation problems discussed in Example 1 (Jingzhou 2013) is known: the equation for x kx ~ 2- (3k-1) x +2 (k-1) = 0. (1) Prove that the equation always has real roots no matter what k is real. (2) If this equation has two real roots x_1, x_2 and | x_1-x_2 | = 2, Find the value of k.