2010·广东汕头·一模
名校
解题方法
1 . 如图,四棱锥
的底面是边长为1的正方形,侧棱
底面
,且
,E是侧棱
上的动点.
的体积;
(2)如果E是
的中点,求证:
平面
;
(3)是否不论点E在侧棱
的任何位置,都有
?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
(2)如果E是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb178784aa857d4d4683e650273f054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(3)是否不论点E在侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509d8dd6031dc0ef92075877e53fe201.png)
您最近一年使用:0次
2024-01-04更新
|
623次组卷
|
5卷引用:广东省2024年1月高中合格性学业水平考试模拟测试数学试题(三)
广东省2024年1月高中合格性学业水平考试模拟测试数学试题(三)陕西省西安市西安中学2023-2024学年高二学考仿真考试数学试题(已下线)汕头市2009-2010学年度第二学期高三级数学综合测练题(理四)2017届北京市海淀区高三3月适应性考试(零模)文科数学试卷(已下线)第13讲 8.6.2直线与平面垂直的性质定理 (第2课时)-【帮课堂】(人教A版2019必修第二册)
名校
解题方法
2 . (1)写出点
到直线
(
不全为零)的距离公式;
(2)当
不在直线l上,证明
到直线
距离公式.
(3)在空间解析几何中,若平面
的方程为:
(
不全为零),点
,试写出点P到面
的距离公式(不要求证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3783208484c038053c9585a1040223a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f341cb234eb3dfe599f4708d08c4545.png)
(3)在空间解析几何中,若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0cbd6b024b3fdff2f5fb5602da1a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf95be25d34a7366bf4060d081329c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2023-12-15更新
|
103次组卷
|
2卷引用:湖北省鄂东南省级示范高中教育教学改革联盟学校2023-2024学年高二上学期期中联考数学试题
名校
3 . 对于正整数集合
,如果去掉其中任意一个元素
之后,剩余的所有元素组成的集合都能分为两个交集为空集的集合,且这两个集合的所有元素之和相等,就称集合
为“平衡集”.
(1)判断集合
是否是“平衡集”并说明理由;
(2)求证:若集合
是“平衡集”,则集合
中元素的奇偶性都相同;
(3)证明:四元集合
,其中
不可能是“平衡集”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffbfa3e226e067ec597ebf0bbc2e87d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c4392f75c09edaec2e70c9eccb2b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e5f6cb6141a374d04b6a14a1b27e282.png)
(2)求证:若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)证明:四元集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a784e0ba1c17aba6990123fe39b89114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a3f266cb6beee27f3d831c1169d3d2.png)
您最近一年使用:0次
解题方法
4 . 一副三角板如图(1),将其中的
沿
折起,构造出如图(2)所示的三棱锥,
为
的中点,连接
,使得
.
![](https://img.xkw.com/dksih/QBM/2023/10/11/3343642308763648/3343931225653248/STEM/64c5aee8e25a473d80c12d50696a2d0d.png?resizew=307)
(1)取
中点
,连接
,设平面
平面
,求证:
;
(2)证明:平面
⊥平面
;
(3)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e6363330b33ca9feda927e6ffd3088.png)
![](https://img.xkw.com/dksih/QBM/2023/10/11/3343642308763648/3343931225653248/STEM/64c5aee8e25a473d80c12d50696a2d0d.png?resizew=307)
(1)取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa4991e049637f9e075989047fb77c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9328c2c8e43ca3363a8aa36d9892fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd227381966b47ed43137a6b5f35582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7717e7e46fc06763d34b20baba892e9b.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
您最近一年使用:0次
名校
解题方法
5 . 如图,在四棱锥
中,四边形
是矩形,
是正三角形,且平面
平面
,
,
为棱
的中点,四棱锥
的体积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/82731e18-73e8-4eec-8bbe-a7741fb478bf.png?resizew=157)
(1)若
为棱
的中点,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
平面
;
(2)在棱
上是否存在点
,使得直线
与平面
所成角的正弦值为
?若存在,求出点
的位置并给以证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5830322dd2824ed012a68f1a2bd9c742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877582b5387278008d14fe5932622fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/82731e18-73e8-4eec-8bbe-a7741fb478bf.png?resizew=157)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b81fb655624ff75a5eab94de9b8c8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3aace91caec728e174daec29a3568ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
名校
解题方法
6 . 问题:已知
均为正实数,且
,求证:
.
证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09f3f04837fc78c3a8cd615d0fa4957.png)
,
当且仅当
时,等号成立.
学习上述解法并解决下列问题:
(1)若实数
满足
,试比较
和
的大小,并说明理由;
(2)利用(1)的结论,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09f3f04837fc78c3a8cd615d0fa4957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ce8e7fbb4c8c728f548bb6c3ae8541.png)
当且仅当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc07ff9c2cb23cfe630c7785ba7ed93b.png)
学习上述解法并解决下列问题:
(1)若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2edfccf9159bb4010669e938f788149b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09ffc1644c7029219b88232145abbdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e32a3a39e310fe224a979e0cafce49.png)
(2)利用(1)的结论,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eace9aecb35ea07662a7f4fe7f75a856.png)
您最近一年使用:0次
2023-11-13更新
|
68次组卷
|
2卷引用:福建省厦门市厦门大学附属科技中学2023-2024学年高二上学期11月期中考试数学试题
21-22高二上·上海浦东新·阶段练习
名校
解题方法
7 . (1)请用符号语言叙述直线与平面平行的判定定理;
(2)把(1)中的定理用反证法证明;
(3)如图,在正方体
中,点N在
上,点M在
,且
,求证:
平面
(用(1)中所写定理证明)
(2)把(1)中的定理用反证法证明;
(3)如图,在正方体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d88aaea5b185ca38fe1026869c7a5fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/20/2851ac28-aed5-411b-976e-90e5e85eaf37.png?resizew=164)
您最近一年使用:0次
2023-10-20更新
|
254次组卷
|
6卷引用:上海市华东师范大学第二附属中学2021-2022学年高二上学期9月质量调研数学试题
(已下线)上海市华东师范大学第二附属中学2021-2022学年高二上学期9月质量调研数学试题(已下线)上海市华东师范大学第二附属中学2021-2022学年高二上学期10月月考数学试题(已下线)10.3 直线与平面平行的判定定理(第1课时)(已下线)第04讲线线、线面、面面平行的判定与性质(核心考点讲与练)(3)上海市敬业中学2023-2024学年高二上学期10月月考数学试题(已下线)第一章 点线面位置关系 专题一 空间平行关系的判定与证明 微点3 直线与平面平行的判定与证明【基础版】
名校
解题方法
8 . 如图所示,底面为正方形的四棱锥
中,
,
,
,
与
相交于点O,E为
中点.
平面
;
(2)
上是否存在点F,使平面
平面
.若存在,请指出并给予证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4ad370fe836accc1b2de6807d8ae62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe2fe5985a27babe0199e1c0865f49a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f92fb805ed4f3b08ced4b8a385fa1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2023-08-12更新
|
927次组卷
|
9卷引用:四川省达州外国语学校2023-2024学年高二上学期9月月考数学试题
四川省达州外国语学校2023-2024学年高二上学期9月月考数学试题陕西省铜川市宜君县高级中学2022-2023学年高一下学期期中数学试题(已下线)第10讲 8.5.3 平面与平面平行-【帮课堂】(人教A版2019必修第二册)广东省茂名市华侨中学2022-2023学年高一下学期段考二数学试卷(已下线)13.2.4 平面与平面的位置关系(1)-【帮课堂】(苏教版2019必修第二册)(已下线)8.5.3 平面与平面平行-同步题型分类归纳讲与练(人教A版2019必修第二册)吉林省长春市东北师范大学附属中学净月实验学校2023-2024学年高一上学期期中质量监测数学试题(已下线)11.3.3平面与平面平行-同步精品课堂(人教B版2019必修第四册)(已下线)专题突破:空间几何体的动点探究问题-同步题型分类归纳讲与练(人教A版2019必修第二册)
23-24高二上·上海·课后作业
9 . 请指出下列各题用数学归纳法证明过程中的错误.
(1)设
为正整数,求证:
.
证明:假设当
(
为正整数)时等式成立,即有
.
那么当
时,就有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b265260b1c40af006ba6f66a11ed576.png)
.因此,对于任何正整数
等式都成立.
(2)设
为正整数,求证:
.
证明:①当
时,左边
,右边
,等式成立.
②假设当
(
,
为正整数)时,等式成立,即有
,
那么当
时,由等比数列求和公式,就有
,等式也成立.
根据(1)和(2),由数学归纳法可以断定
对任何正整数
都成立.
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b502d9c57239d9f42fdf849878018061.png)
证明:假设当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d8963d68c930f5b28cc8b92c43d469b.png)
那么当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b265260b1c40af006ba6f66a11ed576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced66f7e147b6276e1ce9e2b67510141.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8883d7d43d3f61a771d16537c52ac451.png)
证明:①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90bae886c8ab958aa4c693bf8e0627d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90bae886c8ab958aa4c693bf8e0627d.png)
②假设当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2397df3279607612ea3cbef101ee0bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a439aebc27b99718f09e1dff2649482f.png)
那么当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b838d781d5ce98ddcc08af86c1f27ae.png)
根据(1)和(2),由数学归纳法可以断定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8883d7d43d3f61a771d16537c52ac451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,在棱长为2的正方体
中,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/87bb0b53-3cb0-414f-ac51-d843ae06f1fe.png?resizew=154)
(1)求证:
平面
;
(2)证明:
;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/87bb0b53-3cb0-414f-ac51-d843ae06f1fe.png?resizew=154)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5830646a912c3a916beac4f88c116b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4fcf607b0710d12aaabd17fd053d83.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
您最近一年使用:0次