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学会正确解题不可避免地需要熟练掌握概念、公式、定理、方法等以及进行一定数量的解题训练。但是,解题前的仔细审题是正确解题的必要条件。所以,在解题前必须力求避免审题的错误。造成审题错误的原因很多,对于数学问题不注意题中的细微变化,缺乏全面的分析,或仅仅根据形式生搬硬套,常常是导致错误的重要原因之一, 下面拟举数例,说明审题中的“通盘分析,前后联系,句句斟酌,字字推敲”的重要性。例1.(1).1、2、3、4四个数字能组成多少个没有重复数字的四位数? (2)1、2、3、4四个数字能组成多少个没有重复数字的四位偶数。分析:因为组成的四位数中不一定都是偶数,所以这两个题由于一字之差,解法全不相同, 解: (1). P_4~4=24(个)、 (2). 2P_3~3=12(个). 例2.(1).p是什么数值时,方程x~2+px-3=0
Learning to solve problems correctly will inevitably require mastery of concepts, formulas, theorems, methods, etc., as well as a certain number of problem solving exercises. However, careful examination of questions before solving problems is a necessary condition for correct problem solving. Therefore, we must try to avoid mistakes in question before we solve the problem. There are many reasons for the error of the trial question. For mathematics problems, attention to minor changes in the question, lack of comprehensive analysis, or simply applying the form in a rigid way is often one of the important causes of mistakes. The following are a few examples to illustrate in the trial question. The overall analysis, the connection between the front and the back, the sentence, and the importance of words and phrases. Example 1. (1) How many four-digit numbers with no repeatable digits can be formed by four digits of 1, 2, 3, and 4? (2) How many numbers without duplicated numbers can be composed of four numbers 1, 2, 3, and 4? Four even numbers. Analysis: Because the composition of the four-digit is not necessarily an even number, so the two problems due to a word difference, the solution is not the same solution: (1). P_4 ~ 4 = 24 (a), (2). 2P_3~3=12 (units). Example 2. (1) What is the value of p, the equation x~2+px-3=0