零陷阱很隐秘 解题时要注意

• 作 者: 华瑞芬
• 机 构: 安徽省灵璧县黄湾中学,
• 出 处: 数学大世界(初中版)
• 发表日期: 2015年11期
• 关键词: 错解 原命题 数学问题 难以自拔 二次根式 一元二次方程 比例函数 实数根 题设 分类讨论

0这个数看似平凡,可是它在一些数学问题中却有着举足轻重的作用,在解题时稍有不慎,就会掉进与0有关的陷阱之中,难以自拔,导致错解的发生.一平方中的0陷阱例1判断命题“若a>b,则ac~2>bc~2”是否正确?错解∵c~2>0,a>b,∴ac~2>bc~2.所以原命题正确.剖析当c=0时,ac~2=bc~2=0,所以原命题是假命题.

However, it plays a decisive role in some mathematical problems. When it is a little bit tricky to solve a problem, it falls into the trap related to 0 and is hard to extricate itself from it, leading to misunderstandings. A square in the 0 trap Example 1 to determine the proposition “if a> b, then ac ~ 2> bc ~ 2” is correct? Wrong solution ∵ c ~ 2> 0, a> b, ∴ ac ~ 2> bc ~ 2. Therefore, the original proposition is correct. Analysis When c = 0, ac ~ 2 = bc ~ 2 = 0, so the original proposition is a false proposition.