复习教学中,做分类讨论题要异常谨慎,对原题目要多次推敲,看看是否还有隐含条件,这是避免分类讨论导致增解错误的关键所在.例1已知整数k<5,若△ABC的边长均满足关于x的方程x2-3k~(1/2)x+8=0,则△ABC的周长是__.简析:学生解题时,由题意可知△≥0,得k≥32/9,所以32/9≤k<5,又因为k为整数,则k=4.于是x2-6x+8=0,解得x=2或4,从而错解周长为8或10或6或12.除考虑△ABC为等边三角 Reviewing the teaching, to be classified cautiously on the subject of the discussion, the original topic to be considered many times to see if there are still implied conditions, which is to avoid the classification led to the key to increase the error. Example 1 Known integer k <5 , If △ ABC edge length satisfies the x on the equation x2-3k ~ (1/2) x +8 = 0, △ ABC perimeter is __. Analysis: Students solve the problem, we can see from the title △ ≥ 0, so that k≥32 / 9, so 32 / 9≤k <5, and because k is an integer, then k = 4. So x2-6x + 8 = 0, solving x = 2 or 4, Solution perimeter for 8 or 10 or 6 or 12. In addition to consider △ ABC equilateral triangle