《高中数学必修第三章课件基本不等式人教.ppt》由会员分享，可在线阅读，更多相关《高中数学必修第三章课件基本不等式人教.ppt（13页珍藏版）》请在三一文库上搜索。
1、基本不等式基本不等式 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 赵爽弦图是由四个全等的直角三角形所赵爽弦图是由四个全等的直角三角形所 组成，你能找出一些相等关系或不等关组成，你能找
2、出一些相等关系或不等关 系吗？系吗？ 赵爽弦图赵爽弦图 ICM 2002 International Congress of Mathematicians Bejing August 20-28,2002 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Co
3、pyright 2004-2011 Aspose Pty Ltd. a2+b22ab v该结论成立a,b需要什么条件？ 若a,bR，那么 u形的角 度 u数的角 度 a2+b22ab =(ab)20 a0,b0 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd
4、.Copyright 2004-2011 Aspose Pty Ltd. a2+b22ab v公式中等号成立的条件是什么？ 若a,bR，那么 （当且仅当a=b时，取“=”号） u形的角度u数的角 度 当a=b时 a2+b22ab =(ab)2=0 a=b Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 20
5、04-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 若a,bR，那么a2+b22ab （当且仅当a=b时，取“=”号） v你能用文字语言叙述吗？ u数的角度:两个数平方之和不小于该两 数积的2倍 a2+b2 2ab Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.
6、 Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. v如果用 去替换a、b,前提 是什么？能得到什么结论? 若a,bR，那么a2+b22ab （当且仅当a=b时，取“=”号） 问：以下不等式是否成立？ a2+b22ab， a2+b2 2|ab| Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET
7、 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 那么a2+b22 a b那么a + b 2 （当且仅当a=b时，取“=”号） 若aR,bR若a0 b0 问；你能证明吗？ u基本不等式： Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET
8、 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 如图AB是直径，点C是AB上的一 点，设AC=a，BC=b，过C点作 垂直与AB的弦DE,并连接 AD,BD,你能此图几何解释基本 不等式吗 半径不小于半弦 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slide
9、s for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 熟悉运算结构 v我们把 叫做a,b的算术平均数， 把 叫做a,b的几何平均数。 v从形的角度来看，基本不等式具有 特定的几何意义；从数的角度来看 ，基本不等式揭示了“和”与“积”这两 种结构间的不等关系。 v回忆一下你所学的知识中，有哪些 地方出现过“和”与“积” 的结构？ Evaluation only.Evaluation only. Created with Aspose
10、.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 发现运算结构,应用不等式 v试判断 与 2 的大小关系 ？ v如果将条件“x0” 去掉，上述结论 是否 仍然成立？ Evaluation only.Evaluation only. Created with Aspose.Slides for
11、 .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 发现运算结构,应用不等式 v变式1试判断 与 2 的大小关系？ v在结论 成立的基础上，条件“a0,b0” 可以变化吗？ 变式2试判断 与 7的 u 大小关系？ Evaluation only.Evaluation only. Created with Aspos
12、e.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 发现运算结构,应用不等式 v变式3试判断 与 1 的大小关系？ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile
13、5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 你能总结一下吗 （1）重要不等式和基本不等式的条件 及结构 特征 （2）基本不等式在几何、代数二方面 的意义 u知识要点： u思想方法技巧： （1）数形结合思想 （2）换元法、作差法 （3）配凑等技巧 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.