1 . 我们规定:有一组邻边相等,且这组邻边的夹角为
的凸四边形叫做“半等边四边形”.
中,
,
,
,求证:四边形
是“半等边四边形”;
(2)如图2,
中
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
①求
、
的长;
②设
是
所在平面内一点,当四边形
是“半等边四边形”时,请直接写出四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be66a4dad3eda57de0458eec62752245.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ba2098ed6b4137b08932524b72ba37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd95dc30c0344788b94289c464a3158e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d35d8d8bb0dc17f2f86fe5b230a2b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2 . 计算:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25e2b7c62984f4fe9a42d2e39970405.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00810a6bae7e540789dda31f998611b.png)
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3 . (1)计算:
;
(2)解方程:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e437dbd2b87e6c1cd5e3cbfd003a19b5.png)
(2)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b0b663c96a45e8031dde30026ad204a.png)
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4 . (1)计算:
(2)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d71e4de795829227a90715c8854889.png)
(2)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352faf17c7283852f2dab50f5f67e615.png)
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5 . 小明在学习二次根式后,发现一些含根号的式子可以写成另一个式子的平方,如:
,善于思考的小明利用完全平方公式进行了以下探索:
.请你仿照小明的方法解决下列问题:
(1)
,则
______,
_______;
(2)已知x是
的算术平方根,求
的值;
(3)当
时,化简
_______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3197a8f1471dd1d891ad87e622f0e27e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287edec54a2cfc35cc1846fd9a110d8f.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75749425d8cececbf0f1939a171f1562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
(2)已知x是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4324f8b8e4f3dac696bd32eb8e28db42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d882c27ef83f70f8501c6762caf5572.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95842ad442c7f6d5ec4b32939b929e63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5235ff847c0b15b414f2bb4fb3c56600.png)
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6 . 阅读材料:
已知
,求代数式
的值.
解:∵
,
∴
,
∴
,
∴
.
∴
.
请你用上述方法解答下列问题:
(1)已知
,求代数式
的值;
(2)已知
,求代数式
的值.
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d853242ecee89d5578a98d7ee8b9df24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751cd556f0fb490a36f60ccd8d7eae26.png)
解:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d853242ecee89d5578a98d7ee8b9df24.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddbeda56f998f16eb6eceafeb473d85.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b919345af812ebfcb52abd424d696a6e.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34dba17a1f039c0cc6159788d69247e.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9e63789b82065af86cbfb52ce10380.png)
请你用上述方法解答下列问题:
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32deb6b64f19334a54d6af759aa8d9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ecfe9c919b2d86b1ccfc9f4702a47ef.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c86cb753ef281db76db9f9fffea1a998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6948b0629a07c92a49b8440aeac8c325.png)
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7 . 若
为实数,“![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5fc57eadcede31a065a6ab71e015f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
”的运算结果为有理数,则
可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5fc57eadcede31a065a6ab71e015f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 对于任意实数a,b,定义一种运算“
”如下:
.如:
.
(1)
______,
______;
(2)已知
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e14c78f4a7674abd1b4dadb05b2a64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a3a5aa3b559f04fb7b329f10b6dbbf9.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291734d57184327fe56837418e18e8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30271cb8b1173354cb4fb314da85241b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089b9a05e5ce224531f4a7b6de9f5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab60837424e4b3a51549791962b0b98.png)
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9 . 计算:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee43ed4fc7584807c8b56db918ffaa6c.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089fa61e1d154cc8b20f30f9f938fd99.png)
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10 . 计算:
(1)
.
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64ebffc17f74be2d17bceafc11e63ad.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d1e01e4b4b967fd58ec45fdd1f11806.png)
您最近一年使用:0次