论文部分内容阅读
应用题的“列”非常重要,然而有很多耐人寻味、启发思维、形式简单的方程蕴含在“解”的过程中,只有列出解法简捷的方程,才是最佳列法,反之也只有列出的方程形式最简,其解法才最优。下面仅就初中代数二元二次方程组中的应用题为例,说明“列”与“解”的辨证关系。 例1 甲乙两个工程队合做一项工程,12天可以完工,如果甲队单独先做5天后,乙队也来参加,两队再合做9天才完工,两队单独完成这项工程各需多少天?(《代数》第三册P.149,9题) 解:设单独完成这项工程甲队需x天,乙队需y天,由题意按一般列法有方程组:
The “column” of application questions is very important. However, there are many intriguing, inspiring and simple forms of equations that are embedded in the process of “solution.” Only the equations that list the simple and convenient methods of solution are the best ones. The form of the equation is the simplest and its solution is optimal. In the following, only the application problems in the secondary quadratic equations of the junior middle school algebra are taken as an example to illustrate the dialectical relationship between “column” and “solution”. Example 1 The two engineering teams A and B work together to complete a project. It can be completed in 12 days. If A team first does 5 days, B team will also come to participate, and the two teams will work together for 9 days to complete. The two teams complete the project separately. How many days does it take? (“Algebra” Volume III P.149, Question 9) Solution: If you complete this project individually, Team A needs x days, Team B needs y days, and the meaning of the problem is as follows: