(1)已知
,
若
,求
值.
(2)若
,
互为相反数(
不为0),
、
互为倒数,
的绝对值为2,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8cbb247c6ed56338bb6750b9e23bf56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4ca0ea926424a2890b088ae7a24bb46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd039882414ced3cd59d7a4d5ec76f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f2416d1f75a45a314331146550832e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/788f94753d8525c6cabaa7fb41bb0931.png)
更新时间:2023-12-10 21:06:20
|
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【推荐1】请把下面的直线补充为完整的数轴,将下列各数表示在数轴上,并用“
”符号把这些数连接起来:0,
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5756f4f4086a3fddaedef958b2bba49a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7942da6c3fc4005256fb1458557c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e089c43cf0bfd06bd84d19fb10f5af.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/361a17148277a3a856d5344be0726723.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/22/a492808d-eaae-43d6-a304-653f12f7db17.png?resizew=512)
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【推荐2】已知
与
互为倒数,
与
互为相反数,
的绝对值为3,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6616da8f7c03dc5d8f1ed993d3cfa25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b9d9315539052dd2e4a67066d8de1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa19ea47028bd37b399b14e547566e13.png)
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【推荐1】若(x-3)2+|x+y|=0,求出x、y的值.
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【推荐2】定义:在平面直角坐标系
中,已知点
,且
轴,
轴,这三个点中任意两个点之间的距离的最小值称为点
的“近距”,例如:点
的“近距”是3.
(1)已知,
.
①若A,B,C的“近距”是4,则x的值为_________;
②点A,B,C的“近距”的最大值为_________;
(2)已知点
,点
为线段
上一动点,当
,
,
的“近距”最大时,求此时点P的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75193c2de6968a93cf0bffc2f77f807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edcb410ed2b08842ef1780216b8b4df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dda88c548ca0e07daa10a479d83de9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75193c2de6968a93cf0bffc2f77f807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7b9fae7f17043ebf9fb9bedc16da74.png)
(1)已知,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7121bb25c70bc5d4413bb0f24d79a25e.png)
①若A,B,C的“近距”是4,则x的值为_________;
②点A,B,C的“近距”的最大值为_________;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171a54846ede079243b188f5f904e92b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21872d8f6a518e0a2993ccf7a795ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc20df18e2b839068aa2e5889b61310f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21872d8f6a518e0a2993ccf7a795ed2.png)
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【推荐3】阅读理解:
在形如
这一类含有绝对值的方程时,为了去绝对值符号,我们发现两个绝对值符号里面是相同的“
”,可以根据绝对值的意义先对“x”的取值分成
和
两种情况,再去绝对值符号:
①当
时,原方程可化为
,得
,不符合
,舍去;
②当
时,原方程可化为
,得
,符合
.
综合可得原方程的为
.
(1)方法应用:解方程:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff322679c14fc546867b97a014352bf.png)
(2)拓展应用:方程:
;(提示;可以考虑先对“x”的取值进行分类,去了一个绝对值符号后;再对“x”的取值进行分类,去掉另一个绝对值符号)
(3)迁移应用:①求
最小值为______.
②
最小值为______.
在形如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b828ae57a25f3f3aaedb6c844f706c2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e26ea0261f2b67983b07b8d0bb8bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b83a660527359758db64e6566466293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4a7af57545523159f8c77e10f6f915.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b83a660527359758db64e6566466293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ef517650788ec501a02054e4d0e984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b83a660527359758db64e6566466293.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4a7af57545523159f8c77e10f6f915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea84a516750f43f6e14b7394a51faf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cc033406da2cdd342308972c6701f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4a7af57545523159f8c77e10f6f915.png)
综合可得原方程的为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cc033406da2cdd342308972c6701f1.png)
(1)方法应用:解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff322679c14fc546867b97a014352bf.png)
(2)拓展应用:方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e909b70d1cd09ce14286ab4b02aba9.png)
(3)迁移应用:①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafe9766cc7f77f3a6167c278c59efdd.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694737314b2bcf705e49794b65d16b50.png)
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【推荐1】如图,数轴上点
对应的数为
,点
对应的数为
,且
是最大的负整数,
是
的倒数.
(1)求线段
的长.
(2)在数轴上是否存在点
使
?若存在,请求出点
对应的数;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/16/bda6adc2-07d5-4c78-acbe-6d7c41fbbcc0.png?resizew=190)
(1)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)在数轴上是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39fb25442106ecee5147338d1b8aac08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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【推荐2】已知有理数a、b互为相反数且b≠0,c、d互为倒数,有理数m和﹣1在数轴上表示的点相距4个单位长度,求|m|﹣
﹣cd的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b0c79ba29597077ccd4f6473b49b5c.png)
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