在解题过程中,将某一数学对象按照一定的原则或标准分成若干类,然后逐类解决,再把这几类的结论汇总,得出问题的答案.这种解题方法就是分类讨论.分类讨论是“化整为零,各个击破,再积零为整”的解题策略.1.方程中的分类讨论.例1(2013年荆州卷)已知:关于x的方程kx2-(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x1,x2,且|x1-x2|=2,求k的值. In the process of solving problems, a mathematical object according to certain principles or standards into a number of categories, and then class by class, and then summarize these types of conclusions, come to the answer to the problem .This problem-solving method is classified discussion. The disagreement is the solution strategy of “Example 1,” (Jingzhou, 2013) Known: The equation for x kx2- (3k-1) x + 2 (k-1) = 0. (1) Proof: Regardless of the real number k, the equation has a real root; (2) If this equation has two real roots x1, x2 and | x1 -x2 | = 2, find the value of k.