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1、书 山 有 路 勤 为 径，学 海 无 崖 苦 作 舟少 小 不 学 习，老 来 徒 伤 悲 成功=艰苦的劳动+正确的方法+少谈空话天才就是百分之一的灵感，百分之九十九的汗水！天 才 在 于 勤 奋，努 力 才 能 成 功！*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
2、Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.（一）绝对值的定义： 对任意实数a，复习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.问题我们已学过
3、积商绝对值的性质，哪位同学能回答？或 .当 时，有：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.（二）绝对值的几何意义：实数a的绝对值 |a|，表示数轴上坐标为 a的点A到原点的距离（
4、图1）。如：|-3|或|3|在数轴上分别等于点A或点B到 坐标原点的距离。|a| OAxEvaluation 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.由绝对值的几何意义可知，A、B之间的点 与坐标原点的
5、距离小于3，可表示为：即实数x对应的点到坐标原点的距离小于3Evaluation 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.同理，与原点距离大于3的点对应的实数 可表示为：如图Evaluation onl
6、y.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.设a,b是任意两个实数，那么|a-b| 的几何 意义是什么？x|a-b| abABEvaluation only.Evaluation only. Created wi
7、th 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.探究用恰当的方法在数轴上把|a| ， |b| ，|a+b| 表示出来，你能发现它们之间有何关系？定理1 如果a,b是实数，则|a+b| |a| +|b| ，当且仅当ab0时，等号成立。绝对值三角 不等式Evaluation o
8、nly.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.如果把定理1中的实数a,b分别换为向量，能得出什么结论？你能解释其几何意 义吗？探究？(1) 当 不共线时有(2) 当 共线且同向时有绝对值三角 不等式Evalua
9、tion 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.如何证明定理1?探究你能根据定理1的研究思路,探究一下|a| ， |b| ，|a+b|, |a-b|之间的其它关系吗?|a|-|b| |ab|a|+|b
10、|结论: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.注意：1 左边可以“加强”同样成立，即 2 这个不等式俗称“三角不等式”三角形中两 边之和大于第三边，两边之差小于第三边3 同号时右
11、边取“=”， 异号时左边取“=”推论1： 推论2：证明：在定理中以 即： 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.定理探索当 时，显然成立，当 时，要证只要证 ，即证而 显然成立
12、从而证得 . 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.定理探索还有别的证法吗？ 由 与 ，得 .用 可得什么结论？当我们把 看作一个整体时，上式逆Evaluation only.E
13、valuation 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.定理探索证明 吗？能用已学过得的可以 表示为 即即 .就是含有绝对值不等式的重要定理， Evaluation only.Evaluation only. Created wi
14、th 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.例题求证 .例2 已知 ，证明：Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.C
15、reated 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.例题例3 求证 . 证明：在 时，显然成立.当 时，左边 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.练习已知 求证 . 1已知 ，求证 . . ；2已知 ，求证：Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET
