计算
(1)
;
(2)
;
(3)
;
(4)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc94ba396876c7d0f0030d4398e5ea6.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ae9a7da5705f8f4a77de457f8ea80f.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c7d4c2c2e6a6e86fbe905db2568213.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928e5385cc6bd01ddf79f8d25d2df306.png)
更新时间:2021-10-22 08:55:52
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解答题-计算题
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【推荐3】数学教育家波利亚曾说:“对一个数学问题,改变它的形式,变换它的结构,直到发现有价值的东西,这是数学解题的一个重要原则”.
材料一:把根式
进行化简,若能找到两个数m、n,是
且
,则把
变成
,开方,从而使得
化简.
例如:化简![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f52a49827b10ed69c411a4fc24b7ea.png)
解:∵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b2d4b3fc4fe9550d30c5a9936c28a3.png)
∴![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480dcc40b76180b3737febc8b55088d3.png)
材料二:在直角坐标系xOy中,对于点P(x,y)和Q(x,y')给出如下定义:若
,则称Q点为P点的“横负纵变点”.例如点(3,2)的“横负纵变点”为(3,2),点(
,5)的“横负纵变点”为(
,
).
请选择合适的材料解决下面的问题:
(1)点(
,
)的“横负纵变点”为_______;
(2)化简:
;
(3)已知a为常数(
),点M(
,m)且
,点M'是点M的“横负纵变点”,求点M'的坐标.
材料一:把根式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9854e4de421784e749b6cfeda612d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191b0ca0ce0d98e7d040b0d70b23d017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ead83a52c433d9d784148579af0bb4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c78236d96350faf1c842585d9e747e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf058903773624156192980385dde77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9854e4de421784e749b6cfeda612d1.png)
例如:化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f52a49827b10ed69c411a4fc24b7ea.png)
解:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b2d4b3fc4fe9550d30c5a9936c28a3.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480dcc40b76180b3737febc8b55088d3.png)
材料二:在直角坐标系xOy中,对于点P(x,y)和Q(x,y')给出如下定义:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd394149e5f122369e710ff26170a87a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ce3ebd1112220c639562739f1f9d1.png)
请选择合适的材料解决下面的问题:
(1)点(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47153fdd73c0661fa460130082e30929.png)
(2)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dce22e17fbe24452c625bdeba341fad4.png)
(3)已知a为常数(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46b4c7585238f53d85f5a96d35d95af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9db9373e74ecf5d63ad98afe66aa4ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1775b115051900c415988cb14227564.png)
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