1 . 已知
阶方阵
中的各元素均为正数,其中每行成等差数列,每列都是公比为2的等比数列,已知
.
(1)求
和
的值;
(2)计算行列式
和
;
(3)设
,证明:当
是3的倍数时,
能被21整除.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944e7a418f86eef567cf20c196db07dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425dd6d107574d3aab56558cc08d2648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe3785a7ea5220d7e990f08045f25222.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e84c30444f13d37ada78285dc4f83b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3bb6d9c3e9e00ccda6c5ccafefd630.png)
(2)计算行列式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e027dff5c04c837040f5c46422ad24e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358b8c349b8fe30ec98d66febfc76db8.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e82ff47d67bfb5ff6310538189ca49a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963391e1a37b12d40d1bac0b1c9ac4ac.png)
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2 . 已知椭圆
及其上的点
.若直线
交椭圆于A,B两点,直线
,
的斜率为
,
且
,2,
成等差数列,求△
的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e4a41cbe3d1f25154602dee11d36ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5516da98949f4528c7399e4274c34482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e769e2c4c658c63e429e5a8926666504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14f628b1103d160c21b94bfcb55ae46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
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名校
3 . 已知数列
和
满足:
,且
成等比数列,
成等差数列.
(1)行列式
,且
,求证:数列
是等差数列;
(2)在(1)的条件下,若
不是常数列,
是等比数列,
①求
和
的通项公式;
②设
是正整数,若存在正整数
,使得
成等差数列,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaf2a2590bb84d646957f913d78f6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde27adb5a101a9b93235d8b86eafdce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ec2003a74a216d458ebdc960bfe0c61.png)
(1)行列式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff06b8cc52a87bdf84438c2c1b0746f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f0b788c31efa4cba4bf7bcf1821a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d1cadfd6253f1e128caf7b831acdc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213d3cda1a386785262d943037e37255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
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4 . 矩阵乘法运算
的几何意义为平面上的点
在矩阵
的作用下变换成点
,记
,且
.
(1)若平面上的点
在矩阵
的作用下变换成点
,求点
的坐标;
(2)若平面上相异的两点
、
在矩阵
的作用下,分别变换为点
、
,求证:若点
为线段
上的点,则点
在
的作用下的点
在线段
上;
(3)已知△
的顶点坐标为
、
、
,且△
在矩阵
作用下变换成△
,记△
与△
的面积分别为
与
,求
的值,并写出一般情况(三角形形状一般化且变换矩阵一般化)下
与
的关系(不要求证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c158a0dafc1ed72d4cd92ce8be537d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a63c1c60b695b37bec52bfb8bae214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba166b3713688f7e6ef0fbfa2890881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b45d23c105698406d1299177026285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367091d7500780500b0eeb961ed19bda.png)
(1)若平面上的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01fab4a5ee2cd8546c9276d09fcfe346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3346d5fe92ff182b98e2a27b64af0cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若平面上相异的两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee6765a83140d745a6de4c85d9b6b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
(3)已知△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a26e951d6d2369e8da79a793a93a66a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe030690868617d57c0bc82b98ad662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b5956df0cf0f537fe24570a46c7d379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86d62e7455f30b7aad0d137c6b1403d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1264a2e3609e1c274acb89b5ea5019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1264a2e3609e1c274acb89b5ea5019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
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名校
5 . 利用行列式解关于
的二元一次方程组
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6215b48ddcae362f60d5d2623a05f46b.png)
您最近一年使用:0次
2020-03-04更新
|
153次组卷
|
3卷引用:上海市曹杨二中2017-2018学年高二上学期期中数学试题
名校
6 . 在平面直角坐标系
中,已知两点
,若点
的坐标满足
,且点
的轨迹与抛物线
交于
两点.
(
)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf1069dc2a2ff58dbe380d498b45a780.png)
(
)在
轴上是否存在一点
,使得过点
任作一条抛物线的弦,并以该弦为直径的圆过原点.若存在,求出
的值及圆心的轨迹方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296f48fef777ca1d91562090be4d9503.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61a5dfebe72f823765607be6cd57254a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf1069dc2a2ff58dbe380d498b45a780.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/562767e676c51dcbc9aa9ace553ac47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
7 . 已知圆
的极坐标方程:
;直线
的极坐标方程:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178d249d923f64e51ac742a37ce2f292.png)
求圆心
到直线
的距离;
若直线
在矩阵
的交换下得到直线
,求直线
的直角坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdebedd02b4ea57f8562443742086d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178d249d923f64e51ac742a37ce2f292.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88504b2acbff43252ed3fb7e9ec1a7fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8815f2eaf0316e22557bd3cf23dd827f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-12-04更新
|
811次组卷
|
2卷引用:2015-2016学年江苏淮阴中学高二下期中理科数学试卷
18-19高二上·上海浦东新·阶段练习
名校
8 . 设二阶方矩阵
,则矩阵
所对应的矩阵变换为:
,其意义是把点
变换为点
,矩阵
叫做变换矩阵.
(1)当变换矩阵
时,点
、
经矩阵变换后得到点分别是
、
,求经过点
、
的直线的点方向式方程;
(2)当变换矩阵
时,若直线上的任意点
经矩阵变换后得到的点
仍在该直线上,求直线的方程;
(3)若点
经过矩阵
变换后得到点
,且
与
关于直线
对称,求变换矩阵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a72b9c5c237f830cf302e780c8a65ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc163fa0a2929ff019012aa3623088b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ead0c5a16ce4734c9e60838f927e894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)当变换矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103cac0a1fed34ab690764afa75a1bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79fef5c2bdeab99d9d397c2dce4b416d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90b747a0d6458d973963bce3606eb74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
(2)当变换矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e5794bde4de317a991f4e48650eb25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
您最近一年使用:0次
9 . 我们用
(
,
、
、
、
)表示矩阵
的第
行第
列元素.已知该矩阵的每一行每一列都是等差数列,并且
,
,
.
(1)求
;
(2)求
关于
,
的关系式;
(3)设行列式
,求证:对任意
、
,
、
、
时,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef835c9ad2636a9662fb6c99e3abc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57fd1cbade4ecad1fb21cff5b483a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98573a9a667b0eebb101d0811a4e761a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b51541c6afa99ce5e9014e1526c56c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e011468c890dc35be48cea708e3aab2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c439d2937a46028d243b510560821c6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd793520f179479e5573f5b731fac487.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
(3)设行列式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a091345567aacebd45d509e0e5aa2bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9612cb52aacd0b66fc1ba1297267c9c7.png)
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10 . 在中学阶段,对许多特定的集合(如实数集,平面向量集等)的学习常常是以定义运算(如四则运算)和研究运算律为主要内容,现设集合
由全体二元有序实数对组成,在
上定义一个运算,记为
,对于
中的任意两个元素
,
,规定:
.
(1)计算:
;
(2)请用数学符号语言表述运算
满足交换律和结合律,并证明交换律;
(3)
中是否存在唯一确定的元素
满足:对于任意
,都有
成立,若存在,请求出元素
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75bcf6339e9c978b1109a43e75dbc920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e5a3f00c71a8388bddf93eaa74b00a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dfef683de05e5cc1a90635f4a6edd50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e5848b1798d99663bdeac5c9815666.png)
(1)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb93c4b8f07fc687b3119d75fe3c5b1.png)
(2)请用数学符号语言表述运算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75bcf6339e9c978b1109a43e75dbc920.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561e9a85cd4fc7ba728a6669ce017b82.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561e9a85cd4fc7ba728a6669ce017b82.png)
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