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1、绝对值的几何意义【考纲说明】1、理解绝对值的几何意义，了解绝对值的表示法，会计算有理数的绝对值；2、能够利用数形结合思想来理解绝对值的几何意义，根据绝对值的意义及性质进行简单应用。【趣味链接】正式篮球比赛所用球队质量有严格的规定,下面是6 个篮球的质量检测结果，用正数记超过规定质量的克数，用负数记不足规定质量的克数，检测结果为：-20，+10、+12、-8、-11 请指出那个篮球的质量好一些,并用绝对值的知识进行说明。【知识梳理】1、绝对值的定义：在数轴上，一个数所对应的点与原点的距离称为该数的绝对值，记作|a|。2、绝对值的性质：（1）绝对值的非负性，可以用下式表示：|a|0，这是绝对值非常
2、重要的性质；a（a0）（2）|a|=0（a=0）（代数意义）-a(a0)（3）若|a|=a，则 a0；若|a|=-a，则 a0；（4）任何一个数的绝对值都不小于这个数，也不小于这个数的相反数，即|a|a，且|a|-a；（5）若|a|=|b|，则 a=b 或 a=-b；（几何意义）（6）|ab|=|a|b|；|ba|=|ba（b0）；精品w o r d 学习资料 可编辑资料-精心整理-欢迎下载-第 1 页，共 5 页（7）|a|2=|a2|=a2；（8）|a+b|a|+|b|a-b|a|-|b|a|+|b|a+b|a|+|b|a-b|【经典例题】【例 1】（2011 青岛）若ab|ab|，则下列
3、结论正确的是（）A.a0，b 0 B.a0，b0 C.a0，b0 D.ab0【例 2】（2011 莱芜）下列各组判断中，正确的是（）A若|a|=b，则一定有a=b B.若|a|b|,则一定有ab C.若|a|b，则一定有|a|b|D.若|a|=b，则一定有a2=(-b)2【例 3】（2011 日照）有理数a、b、c 在数轴上的位置如图所示，则式子|a|+|b|+|a+b|+|b-c|化简结果为()A2a+3b-c B 3b-c Cb+c D c-b【例 4】（2009 淮安）如果aa|，下列成立的是（）A0aB0aC0aD0a【例 5】（2008 扬州）在数轴上，点A 所表示的数为2，那么到点
4、A 的距离等于3 个单位长度的点所表示的数是.【例 6】（2010 南京）数轴上分属于原点两侧且与原点的距离相等的两点间的距离为5，那么这两个点表示的数为_.【例 7】（2010 泰安）已知a 是有理数，|a2007|+|a2008|的最小值是 _【例 8】绝对值小于3.1 的整数有哪些？它们的和为多少？【例 9】（2012 盐城）|x|=4，|y|=6，求代数式|x+y|的值.【例 10】（2012 宿迁）已知：|x-2|+x-2 0，求：(1)x+2 的最大值；(2)6-x 的最小值.精品w o r d 学习资料 可编辑资料-精心整理-欢迎下载-第 2 页，共 5 页文档编码:CH2Q5I
5、8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN
6、8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I
7、8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN
8、8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I
9、8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN
10、8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I
11、8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3【课堂练习】1、（2012 镇江）若ab，且|a|b|，则下面判断正确的是（）A.a0 B.a0 C.b0 D.b0 2、（2008 合肥）|x-2|+|x-1|+|x-3|的最小值是()A1 B2 C3 D4 3、（2009 常州）绝对值大于或等于1，而小于4 的所有的正整数的和是（）A.8 B.7 C.6 D.5 4、数轴上表示数5和表示14的两点之间的距离是_.5、（201
12、0 曲阳）若|x-3|=3-x，则 x 的取值范围是 _.6、（2009 南通）若|a-2|2-a，求 a 的取值范围.【课后作业】1、下列代数式中，值一定是正数的是()Ax2B.|x+1|C.(x)2+2 D.x2+1 2、若 a为任意实数，则下列式子中一定成立的是()A|a|0 B|a|a C.aa1D.01a3、若|x+1|+|2x|3，则 x 的取值范围是 _4、|x2|x5|的最大值是 _，最小值是 _5、绝对值大于2.1 而小于 4.2 的整数有多少个？精品w o r d 学习资料 可编辑资料-精心整理-欢迎下载-第 3 页，共 5 页文档编码:CH2Q5I8O9C4 HW8A8V
13、3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编
14、码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V
15、3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编
16、码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V
17、3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编
18、码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V
19、3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K36、设 a，b 是有理数，则|a+b|+9 有最小值还是最大值？其值是多少？7、求满足关系式|x-3|-|x+1|4 的 x 的取值范围8.已知 a-20b2，去掉下列三式的绝对值符号：精品w o r d 学习资料 可编辑资料-精心整理-欢迎下载-第 4 页，共 5 页文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8
20、 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2
21、Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8
22、 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2
23、Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8
24、 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2
25、Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8
26、 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3【参考答案】【经典例题】1、D 2、D 3、C 4、D 5、5 或-1 6、2.57、1 8、0，1，2，3，和为 0 9、2 或 10 10、(1)当 x2 时，x+2 得最大值 2+24；(2)当 x 2 时，6-x 得最小值 6-24【课堂练习】1、C 2、B 3、C 4、9 5、x 3 6、a2【课后作业】1、C 2、D 3、1 x 2 4、3，-3 5、3，4，有 4 个6、有最小值9 7、x-1 8、2a，()ab，2bab精品w o r d 学习资料 可编辑资料-精心整理-欢迎
27、下载-第 5 页，共 5 页文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:C
28、H2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7
29、V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:C
30、H2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7
31、V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:C
32、H2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3文档编码:CH2Q5I8O9C4 HW8A8V3B7V8 ZN8F1Z1T8K3