计算题.
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa21525f42e97ebcd56b0237fdb497a9.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a2d35eb74aaef617c5eda697ec8b2e.png)
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288fa44d2f5e9544930b379d6f1e3392.png)
(4)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa21525f42e97ebcd56b0237fdb497a9.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a2d35eb74aaef617c5eda697ec8b2e.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288fa44d2f5e9544930b379d6f1e3392.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87da55b87e46eae0453ccbf5d3b526a4.png)
更新时间:2023-07-18 11:03:31
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【推荐2】有理数a、 b、 c在数轴上的位置如下图所示:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/3/36a20f2d-b5e1-446a-b37b-905f1769f25a.png?resizew=242)
(1)比较
、 b、 c的大小(用“
”连接) ;
(2)化简
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/3/36a20f2d-b5e1-446a-b37b-905f1769f25a.png?resizew=242)
(1)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5060ad37c403f248c937c1d59af5c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7942da6c3fc4005256fb1458557c0.png)
(2)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38318f0db999f3bf95cb4808ec813f05.png)
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【推荐1】阅读下面材料并解答问题
材料:定义:如果将一个分式能化成一个整式与一个分子为常数的分式和的形式,则称这个分式为“和谐分式”.如:将分式
拆分成一个整式与一个分式(分子为整数)的和的形式.
解:由分母为
,可设
,
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247002f10e3b5ab31b869732d266236b.png)
∵对任意
上述等式均成立, ∴
且
,∴
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
∴![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c8a5de305760a5aebcf7e2c8aa5d90.png)
这样,分式
被拆分成了一个整式
与一个分式
的和.
求:
(1)如果分式
的值为整数,求
的整数值.
(2)当
时,求出
的最小值.
材料:定义:如果将一个分式能化成一个整式与一个分子为常数的分式和的形式,则称这个分式为“和谐分式”.如:将分式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ab013655fa8c0cab71bf7a6af39e86.png)
解:由分母为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449acf863af31e82bd0ff0fd2a180951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661500b2fe9d83a2d4206854c2bec604.png)
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247002f10e3b5ab31b869732d266236b.png)
∵对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8792eaab0b6464e5d07436c64aa751a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c8a5de305760a5aebcf7e2c8aa5d90.png)
这样,分式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ab013655fa8c0cab71bf7a6af39e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39241f2eeccaa16d0550d851619bcb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd429b8e5e7fb030b585ca0148718ab4.png)
求:
(1)如果分式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3f7cea59d436140c19078f1309dc01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b88e53e6ca674b4cb92ba78dddf989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ab5928bcba9387827236db724195f1.png)
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【推荐2】爱动脑筋的南南在做二次根式的化简时,发现一些二次根式的被开方数是二次三项式,而且这些二次三项式正好是完全平方式的结构,于是就可以利用二次根式的性质:
来进一步化简.比如:
,∴当
,即
时,原式=
;当
,即
时,原式=
.通过进一步思考,南南发现,像
这样的二次根式,可以通过变形成
这样的形式后,通过构造成完全平方式
的结构即可化简为
,就可以进行后续计算.
(1)仿照上面的例子,请你尝试化简
.
(2)化简:
=__________;
=__________.
(3)解方程:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dbd4595fc0937334366a716ce50df70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c9360adb7f71699122098b1ef36c34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f505a21a44ddbb3427122e008bef82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a380067a20c25338eb0312e8df6c2760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83666674f1111c699d7c5f7b792e0285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129a17e41f6d3855ee2a68544ab808bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002ad1638f25e355d70d5ab63e637f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ea85da6ab2bc74ecff52381fbe816c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f52a49827b10ed69c411a4fc24b7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5b65505010a273a01f7b91130a3535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0065eb43d02804269cb3b45d72f2b31c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2617461cdd1422313556bcaa31c4661.png)
(1)仿照上面的例子,请你尝试化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/461314d3820e8d6b64b91bf20f06bcd0.png)
(2)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711e50b812b6da54e5ba6096d3c1f210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db9a75e939ca25663a9a16619a91085.png)
(3)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333585cf54f27ddb66405f724f85865e.png)
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