1 . (1)计算:
;
(2)已知
,求x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a368602ca15cbc21efede7d803e94067.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b729beeeadb28ebda304f4a679c493e.png)
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2 . 计算或求
的值:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea37ff315d89e4f1e1ccbacfea1d66f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cd9e9944f0cda57989d3ab88137139a.png)
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3 . 计算:
(1)计算:
;
(2)解方程:
.
(1)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3b584fa31319941d42c4a27877358f.png)
(2)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df80fa1080d59810f595985f3573264.png)
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4 . 定义:我们将
与
称为一对“对偶式”.
因为
,可以有效的去掉根号,所以有一些题可以通过构造“对偶式”来解决.
例如:
,所以
与
互为“对偶式”.
(1)
的“对偶式”是________,
的“对偶式”是________.
(2)已知
,其中
.
①
的“对偶式”的值是________.
②利用“对偶式”的相关知识,求方程
中x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9928ba39cdd5878aced506d3dbb9fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b87033f1efe85e559a9a3efc985be9d.png)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50036f42d68bcb48ee54bf6a8e76856f.png)
例如:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9716b80c5256540830bd48ad968f5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e833d2c9f895f404a733a7d389e3b07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acba2d76c389f6f53cc8cf757760cd02.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77abd3f77c42e53acb598fbc64cc22f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63319272787a2c3137212e4d11b0e887.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c3a00640f05c28e85b3d2e2ba562f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d16f50c58699f352885df1f7bc9132.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63319272787a2c3137212e4d11b0e887.png)
②利用“对偶式”的相关知识,求方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c3a00640f05c28e85b3d2e2ba562f9.png)
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5 . 计算题
(1)计算:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9963da8600a163165f32c7bc687166.png)
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/462ede583e9d8f373fef22f55ca37251.png)
(2)求x的值:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1cc1379b47c1e5e8db535a51cda6c9.png)
②
(1)计算:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9963da8600a163165f32c7bc687166.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/462ede583e9d8f373fef22f55ca37251.png)
(2)求x的值:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1cc1379b47c1e5e8db535a51cda6c9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8108c685f554315c1f1fa34153ffbae2.png)
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6 . (1)计算
;
(2)求式中x的值.
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14992d7e630fb29b3c896596c5a17f7e.png)
(2)求式中x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cccab15dc6e41ef9fec612f6d1629ccd.png)
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7 . (1)计算:
,
(2)解方程:
,
(3)解方程组:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2ca2a91c4380ae7e7a847d32d55aa6.png)
(2)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1117fd3baae250c3cc15ada438b07a10.png)
(3)解方程组:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1dd07714d9810007e7699133607595.png)
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8 . 求下列各式中x的值:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152f6ba565a241bbb53f31a7f4ab536f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/393b40a2fdedb540f7d33f65f0d757d2.png)
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名校
9 . (1)已知,一个正数的两个平方根分别为
和
,求m和这个正数;
(2)已知a是
的小数部分,b是
的整数部分,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7610524671d0a762d423b20d7e0ce1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd749fe1cc2797b017c7fafad9ab356.png)
(2)已知a是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619096595112f0340a43b756e114dd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20838e72faf737614d76fcee82ab6c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897aeafa8da0737baa70f64fdf55c269.png)
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10 . (1)计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a3f53dc1dda68a86c4ad1025220b608.png)
(2)求式中x的值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a3f53dc1dda68a86c4ad1025220b608.png)
(2)求式中x的值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9adcc3a56ec62fc2109f5d90a3b37caa.png)
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