已知a为有理数,那么代数式|a﹣1|+|a﹣2|+|a﹣3|的取值有没有最小值?如果有,试求出这个最小值:如果没有,请说明理由.
更新时间:2018-11-25 22:34:08
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【推荐1】(1)
的最小值等于________;
(2)
的最小值等于________;
(3)
________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0a02595228c8884f2090ba5a22df58.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4963944893315709cfb45bc68c721bf5.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ef8da04837f3064fcbcc69bc6e1206.png)
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【推荐2】对于有理数a,b,n,d,若
,则称a和b关于n的“相对关系值”为d,例如,
,则2和3关于1的“相对关系值”为3.
(1)
和6关于2的“相对关系值”为 ;
(2)若a和3关于1的“相对关系值”为7,求a的值;
(3)若
和
关于1的“相对关系值”为1,请求出
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd84741719a22af5ac3d671af99fb812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47fbba19405d71c259852344e314fa41.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
(2)若a和3关于1的“相对关系值”为7,求a的值;
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222c12bccd0b40100273e4a4f7aa3948.png)
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【推荐3】如图,已知数轴上点
表示的数为
,
是数轴上位于点
左侧一点,且点
与点
的距离为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/89d6c52c-55d9-4e1b-809d-3bec65302104.png?resizew=163)
(1)写出数轴上点
表示的数__________;
(2)
表示
与
之差的绝对值,实际上也可理解为
与
两数在数轴上所对的两点之间的距离.
如
的几何意义是数轴上表示有理数
的点与表示有理数
的点之间的距离.试探索:
若
,则
__________;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
的最小值为__________.
(3)动点
从
点出发,以每秒
个单位长度的速度沿数轴向右匀速运动,设运动时间为
秒,当
__________,点
,
两点之间的距离为
;
(4)动点
,
分别从
,
两点,同时出发,点
以每秒
个单位长度沿数轴匀速运动,
点以
个单位速度,沿数轴匀速运动,设运动时间为
秒.当
,
之间的距离为
时,则
的值为__________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e60fbe6820130fb20abc555a94b5ea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/89d6c52c-55d9-4e1b-809d-3bec65302104.png?resizew=163)
(1)写出数轴上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4adb0fe30e6a27e2d212536fd76fafc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2b0af17241d77dc875ce0ad97ef7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31562c66e57c5a0940ed3e8e2aaea4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678ca4f156bb4bea3cbcb577b522afa1.png)
(3)动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(4)动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf4b43b6792b9ae78a1c8cae4e60524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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