已知
,
互为倒数,
,
互为相反数,
,求
的值.
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a4b7ecb4712c4d6641dde7aaa494fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b919291c830005c53bb4cfd85b6bc9f.png)
更新时间:2022-12-07 14:09:32
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【推荐2】昨天,小明把老师布置的作业题忘记了,只记得式子是
,小亮告诉小明,
是最大的负整数,
的相反数是2,
的相反数和绝对值都是它本身.请你帮小明解答下列问题:
(1)写出
,
,
的值;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c1640c53ba10239eb4f6d2ed2f08c8.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/071a7e733d466949ac935b4b8ee8d183.png)
(1)写出
![](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/071a7e733d466949ac935b4b8ee8d183.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a81b62b9379f916218e2ca479144a0.png)
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【推荐2】知识理解:同学们,我们在绝对值一节的学习中知道,一般的,数轴上表示数
的点与原点的距离叫做数a的绝对值,绝对值符号中含有未知数的方程叫做绝对值方程.像
,
,
都叫做绝对值方程,对于绝对值方程,我们根据绝对值的定义求出未知数的值.
例如:
(1)
表示在数轴上,数a与数0的距离为5个单位长度,所以,
或
,对应的数有两个,分别是5和
.
解:因为
,所以,
或
.
(1)
表示在数轴上,数a与数3的距离为5个单位长度,所以,
或
,对应的数有两个,分别是8和
.
解:因为
,所以,
或
,解得:
或
.
知识应用:
(1)求出下列未知数的值.
;
.
(2)知识探究:
直接写出
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7966da1ca145c20afeac6273d72e54fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b23bc10f7383b6f0f821c148193964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1615215a4eb3b355f9bfdc0ab233d3f9.png)
例如:
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06e16c10eb0516c0db55afbce431510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4f17f1c10f7b8cb2a979f4ee26a307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbf4c1ff85747945b9e99b64b55983a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ce3ebd1112220c639562739f1f9d1.png)
解:因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d23fa09f36fec8353a4d5ecfdd7786b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab839d8569171afab5ed55c22013aa72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a81e971f501d78f5560c0c3d42f0f6.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a0cada10b9a37538d174a22ca3cb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1feae6b72a41196a96ebbcfd7f4e343d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b629f9aa85d932d1c6be6c71e693320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
解:因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a0cada10b9a37538d174a22ca3cb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1feae6b72a41196a96ebbcfd7f4e343d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b629f9aa85d932d1c6be6c71e693320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e15cbd7c42d7b15d7ba8d2b28ab8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
知识应用:
(1)求出下列未知数的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/337033d1d40e766f4ac09bcff8fb1363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dde0fe42f595fde68e635b02858862.png)
(2)知识探究:
直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179cd6cd022f0514c354b1467691f6fd.png)
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【推荐3】数轴上表示有理数a,b,c,d的点的位置如图所示:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/49690469-3ffd-47de-a3d0-e4f4d1144f60.png?resizew=184)
(1)请将有理数a,b,c,d按从小到大的顺序用“<”连接起来:_______________________;
(2)如果︱a︱=4,表示数b的点到原点的距离为6,︱c︱=2,c与d距离原点的距离相等,则a=________,b=________,c=__________,d=__________;
(3)在(2)的情况下,如果有一蚂蚁位于有理数a表示的点的位置,要爬行到距离原点5个单位长度的位置,请说明这只蚂蚁应该如何爬行?
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/49690469-3ffd-47de-a3d0-e4f4d1144f60.png?resizew=184)
(1)请将有理数a,b,c,d按从小到大的顺序用“<”连接起来:_______________________;
(2)如果︱a︱=4,表示数b的点到原点的距离为6,︱c︱=2,c与d距离原点的距离相等,则a=________,b=________,c=__________,d=__________;
(3)在(2)的情况下,如果有一蚂蚁位于有理数a表示的点的位置,要爬行到距离原点5个单位长度的位置,请说明这只蚂蚁应该如何爬行?
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【推荐1】若a、b互为相反数,c、d互为倒数,m的绝对值是2.
(1)直接写出
,
,m的值;
(2)求
的值.
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6c5ec685e8420a8672cefa43e45869.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed7bf7c1a4c8462bb28276f42895c7d.png)
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【推荐2】若a,b互为相反数,c,d互为倒数,则关于x的方程(a+b)x²+3cd(x+1)
3的解为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c44e0542b8df0e8ea7998b5cc33a288.png)
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【推荐1】如果一对数
,
,满足
我们称这一对数
,
,为“伴随数对”,记为
;如果一对数
,
,满足
,我们称这一数对
,
为“和谐数对”,记为
.
(1)若
是“伴随数对”,则
____;
(2)若
是“伴随数对”,则m=__ ___;(用含
的代数式表示)
(3)若有一数对
,
既是“伴随数对”,也是“和谐数对”,求
,
的值;
(4)若
是“伴随数对”,
是“和谐数对”,求式子
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f89f6ffb8906d19bf8b0baf13879f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.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/5a8641de131e86041bb4cee948569cdc.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/f030c36bb8786df88d401792062a4100.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e11887a207fc2fb2380bedaa2cc37da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若有一数对
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cffbfd0d0d37d8bc7b1977f383b9b9f.png)
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