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波利亚在《怎样解题》一书中给出数学解题的四个步骤:理解题意、拟定计划、执行计划、回顾.他在“回顾”中告诫我们:“你能在别的什么题目中利用这个结果或这种方法吗?”学习数学就应该在一定程度上理解其本质,掌握其方法和规律,继而“解一题,会一类,通一片,得一法”.笛卡尔也说过:“我所解决的每一个问题将成为一个范例,以用于解决其他问题.”这个“范例”往往是通性通法,即通解.追求通解,提炼通解,应用通解是学习数学的不懈追求.本文以证明线段等式a·b±c·d=e·f的通解为例,供参考.一、证明形如a·b±c·d=e·f等式的通解
In the book “How to Solve a Problem”, Polya gives four steps in mathematics problem solving: understanding the meaning of a problem, drawing up a plan, executing a plan, and reviewing. He told us in the “Review”: “You can What other topic use this result or this method?”Learning mathematics should understand its essence to a certain extent, grasp its methods and laws, then “solution a question, will be a class, pass a piece, get a Act ”. Descartes also said: “ Every problem I solve will become an example to solve other problems.” This “example ” is often a general approach, that is, a general solution. General solutions, general solutions, and general solutions are the untiring pursuits of learning mathematics. This paper uses the general solution of the line segment equation a·b±c·d=e·f as an example for reference. I. Prove that the shape is like a·b±c· General solution of d=e·f equation