1 . 完全平方公式:
,
是多项式乘法中的重要公式之一,它经过适当变形可以解决很多数学问题
例如:若
,
,求
的值.
解:
.
根据以上信息回答下列问题:
(1)若
,
,求
的值;
(2)若
,
,求
的值;
(3)如图,长方形
的面积为6,
.在长方形
外分别以
,
为边作正方形
和正方形
,在长方形
内以
,
为边分别作正方形
和正方形
.若阴影部分的周长为38,求阴影部分的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d351a97edcc0783d8d7a02d041bdb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194c8e87fbce2ab6bae776f4631414fa.png)
例如:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7dbc702617c765a573961953cc0901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925be255ca736a53b24d13ddede1a86.png)
解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da19f35b1cfcff8a6f57716d21c8f464.png)
根据以上信息回答下列问题:
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e067be545a0178382625422a2e67621d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f21434bba594ab7da7f0e9f7c294282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09276d499e57788c7e669fc4059c22b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c113e660bc0bd93b5db9b6d75d55f61f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ec08be6e5edde3502faba89bb505e0.png)
(3)如图,长方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b3a0c15f277853d96a0bb908f267c4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae996f17c142d99dd990efb01c39621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ab4fdfc612c9fa2dd8ae24904192d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7502d9ae80577f31638395b64cc901.png)
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2 . 如图,A、B、C、D四张卡片分别代表一种运算,例如,5经过
顺序的运算,可列式为:
,8经过运算顺序
运算,可列式为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8b530aae81c84964c6344de10e48a3.png)
(1)请计算
;
(2)列式计算
经过
顺序的运算结果;
(3)若数x经过
顺序的运算,结果是12.则求初始数字x是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4853b4705dee3de86e18a346ee3ae853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dabd4399c15782d4383b6e1ebdfe678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a270f93bce2f40f9517e449495d26c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8b530aae81c84964c6344de10e48a3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/17/6b3cf041-33bb-493f-98c4-eca631c743df.jpg?resizew=271)
(1)请计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dabd4399c15782d4383b6e1ebdfe678.png)
(2)列式计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7802883178112002845956eeefcd6712.png)
(3)若数x经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d28770a3cf80d7886d6845fc9f4bc7db.png)
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3 . 【阅读理解】
【材料一】
是无理数,而无理数是无限不循环小数,因此
的小数部分不可能全部写出来,但可用
来表示
的小数部分.因为
的整数部分是1,将这个数减去整数部分,差就是小数部分.由此得到一个真命题:
如果
,其中a是整数,且
,那么
,
.
【材料二】已知x,y是有理数,并且满足等式
,求x,y的值.
解:∵
,
∴
.
∴
且
,解得:
,
.
请解答:
(1)如果
,其中m是整数,且
,那么
______,
______;
(2)如果
的小数部分为a,
的整数部分为b,求
的值;
(3)已知x,y是有理数,并且满足等式
,求
的值.
【材料一】
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34e01955f8c8fe2f0041b35d8d602a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9ec2b0b6702a5f37fe8a213193dac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e84dbb03e8c627ff11d5c7aeb0c8b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a100443e47f3bd8ff48866627c5a7b.png)
【材料二】已知x,y是有理数,并且满足等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe00100e26241feb17cd1cb89eac8651.png)
解:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe00100e26241feb17cd1cb89eac8651.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585cc515121fe121df0224b16f310e57.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a341b2ea03c3a4f83fb27ff954d60c08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/816d06ecd04291d5e52cc2c954382641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
请解答:
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/723bf2951cdc7eda95fb063854c5c5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a7f63eed0d5e6cfdcb35483f09c3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d83024443ba4361019cfb30537075e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04eae8fe19474b653c5543b20044dc9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/989342e5735d28884e4e3607a77420ba.png)
(3)已知x,y是有理数,并且满足等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d53bfbee43ef84771d82fd5330484c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
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4 . 若x满足
,求
的值.
解:设
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/748c89266828de308c8049015c7f0ca5.png)
∴
.
请仿照上面的方法求解下面问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/18/f0591e24-569d-4654-89b5-5ea456f54ef4.png?resizew=164)
(1)若x满足
,求
的值;
(2)若x满足
,求代数式
的值;
(3)已知正方形ABCD的边长为x、E、F分别是AD、DC上的点,且
,长方形EMFD的面积是48,分别以MF、DF作正方形,求阴影部分的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e5c36c5bb7446be6e5027a27d8607d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/492d2922dbba102b50f89948766c4d15.png)
解:设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab88fdc36b2312b47ab44ed619a70c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/748c89266828de308c8049015c7f0ca5.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf8186851e3272a9690b11dc30ed4e4.png)
请仿照上面的方法求解下面问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/18/f0591e24-569d-4654-89b5-5ea456f54ef4.png?resizew=164)
(1)若x满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9900050f3c51abf23617fa5553eb8524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d3a735d04bfb4d940c0ab1e49cea4d.png)
(2)若x满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcabafc840e06614ec967fef7544228e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fced3a88b80a195bc26d75cdaca3fe3c.png)
(3)已知正方形ABCD的边长为x、E、F分别是AD、DC上的点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ee4cbbb6c003435e0311c0735d0a64.png)
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2022-08-17更新
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8卷引用:江苏省宿迁市宿城区2021-2022学年七年级下学期期中数学试题
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