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数与形是数学中两个最古老而又最基本的对象.将抽象的数与直观的形双向联系与沟通,可使抽象思维与形象思维有机地结合起来,化抽象为形象,从而达到化难为易的目的,本文介绍如何巧用数形结合法证明不等式,供大家参考. 一、构造直角三角形几何模型证明不等式例1求证:3~(2/1)+8~(2/1)>1+10~(2/1). (人教版新教材高二数学上册第30页复习参考题六第7题)
Numbers and shapes are the two oldest and most basic objects in mathematics. The two-way connection and communication between abstract numbers and intuitional forms can organically combine abstract thinking and image thinking, and transform abstract images into images, thus achieving For the purpose of difficulty, this article describes how to use the combination of number and shape to prove the inequality for your reference. I. Constructing a right-angled triangle geometry model to prove inequality Example 1 Verification: 3~(2/1)+8~(2/1)> 1+10~(2/1). (PEP Teacher’s Book of Mathematics for Senior High School, Vol.2, Volume 30, Review of Question 6, Question 7)