1 . 如图,抛物线
与
轴负半轴交于点
,与
轴正半轴交于点
,与
轴交于点
,
.
(1)求抛物线的解析式;
(2)设
是第四象限内抛物线上的点,连接
.
①求点
的坐标;
②连接
,若点
是抛物线上不重合的两个动点,在直线
上是否存在点
(点
按顺时针方向排列,点
按顺时针排列),使得
且
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7b50361cfc74af7a250e058f8c0c9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2a988dc9f03fffcd8acb720d706e9c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/9/72af2cf6-46f5-4831-b8b4-a2f336555c3e.png?resizew=278)
(1)求抛物线的解析式;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d928a3bcf169c67c51a9006f6d29dc67.png)
①求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
②连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd17f1c6f82c15d141ef817a636af90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dac152e5e7d8f9549fbc04c1d42bbfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/332ff50725ece7eb1ac731431768289b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6556d1de4797ef7549a8d983f2da99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877260f1b1ff5dda376e1cefb9f5e9bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 如图,在平面直角坐标系中,直线
经过点
,与
轴正半轴交于
点,与反比例函数
交于点
,且
轴交反比例函数
于点
.
(1)求
的值;
(2)如图1,若点
为线段
上一点,设
的横坐标为
,过点
作
,交反比例函数
于点
.若
,求
的值.
(3)如图2,在(2)的条件下,连接
并延长,交
轴于点
,连接
,在直线
上方是否存在点
,使得
与
相似(不含全等)?若存在,请求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87aba319e62dd0fe1c2db30759a8ded7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d57173ef4cd72eb270686875dfd623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03517310ea1e913f709753592ac65ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e03375e9fa2a949058828f5a5ecce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03517310ea1e913f709753592ac65ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/8e09502e-c5ba-434f-bcf3-b16fb8f38112.png?resizew=477)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a389234de46c9654804bada595264b.png)
(2)如图1,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d64d857c9e44dc69b19e1587e2aa677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03517310ea1e913f709753592ac65ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f72423bf19b975448fd2a0eb4b4cbd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)如图2,在(2)的条件下,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4e5962cfb17195352c899ddcd1650f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0526c0ac1d69705e031d1dbf95dd5220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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3 . 集合
由有限个实数组成,定义集合
的离距
如下:实数轴上,集合
中的每个实数
对应一个点
,实数
对应的点
与所有这些点
的距离的算术平均数记为
,称函数
的最小值为集合
的离距,记为
.例如,集合
的离距是0,集合
的离距是2.
(1)分别求出集合
的离距;
(2)求数集
的离距;
(3)已知非空数集
满足
,试写出一个关于
的大小关系的等式或不等式,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdb777c90f9cabba8d4ed34c16f4acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e51c8010a4568d7d44f261973dea420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdb777c90f9cabba8d4ed34c16f4acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39412925212a989c503e891db840609d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c6fed9c3cf2c00ba1823c3f0a05615.png)
(1)分别求出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7384a3e8b9a7ffb00bb124ba97b7c992.png)
(2)求数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22accc2928d3370f48a84cc4703a4b07.png)
(3)已知非空数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21e6c4bb62b14f8e70d8f8b1ac911bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3598ab9c4ac9a9496c5f34b9b5fda3cf.png)
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名校
4 . 图一所示,在平面直角坐标系中,抛物线
与x轴交于
,
两点,与y轴交于点C.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/60680793-2af4-4c55-a4e2-b4f9dc9eba59.png?resizew=120)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/f93df309-e8e7-4e20-b34d-80be466866ee.png?resizew=119)
(1)求抛物线的函数表达式及顶点坐标;
(2)点P为第三象限内抛物线上一动点,作直线AC,连接PA,PC,求
面积的最大值及此时点P的坐标;
(3)设直线
:
交抛物线于点M,N,求证:无论k为何值,平行于x轴的直线
:
上总存在一点E,使得
为直角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/818ccf8040f189fff5665ec93892b2ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a525534689bd2701205d4ab17574c39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/60680793-2af4-4c55-a4e2-b4f9dc9eba59.png?resizew=120)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/f93df309-e8e7-4e20-b34d-80be466866ee.png?resizew=119)
(1)求抛物线的函数表达式及顶点坐标;
(2)点P为第三象限内抛物线上一动点,作直线AC,连接PA,PC,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7cd2f34acbf4884ac6ea40b5d5be19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216be086e1952cf1e782a7a3c132496e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/435f30095577dc714634354f5ad27715.png)
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名校
5 . 函数
,
,
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a3cf59aa7689deb9e12e993f6b1035b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a711cdf32a16033d2fd9c934051f0cf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf59fcff239eaecc1e7e3df86146c8c.png)
A.函数![]() |
B.设方程![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() ![]() ![]() |
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6 . 若函数
的定义域为
,且对于任意的
、
,“
”的充要条件是“
”,则称函数
为
上的“单值函数”.对于函数
,记
,
,
,…,
,其中
,2,3,…,并对任意的
,记集合
,并规定
.
(1)若
,函数
的定义域为
,求
和
;
(2)若函数
的定义域为
,且存在正整数
,使得对任意的
,
,求证:函数
为
上的“单值函数”;
(3)设
,若函数
的定义域为
,且表达式为:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1c302b2795ab6ffdff6ddedfbc9151.png)
判断
是否为
上的“单值函数”,并证明对任意的区间
,存在正整数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4133958c09fdd82cda8838c9cf46ccda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e2551c314c6ea951fca591bf87a6f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f333263260646c494225db8a7476c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4133958c09fdd82cda8838c9cf46ccda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c3ef724cecaca2c47141a7452bad48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd566272839f638c5b48dcf5edc35a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d257428bd196ea9e5cfbeb2d2f6f4661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395546dd7fb33049b1d09d2b5003fb4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e685edd2226794e07c27f60acec2c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb28ebc468753b283263e00c58aa997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6784497e216821ec890709fce195bdf2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c07bd1bced5e02c11b99392f9526f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d763f5dcb06bdef78c3f5cad865512cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47f9ff9211107eb5e1a489808924e79.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e38e963a27eede8d0f18d28ebb1f06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e436ea3ddcd13e69171135f0ff8e934a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf87d9d48c3de0a5e9f1a70e51a0bef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1c302b2795ab6ffdff6ddedfbc9151.png)
判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf87d9d48c3de0a5e9f1a70e51a0bef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d3149d8dcbd4b02826aece85e2c4a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdb50120ff445d7b2fd13497d18381ca.png)
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解题方法
7 . 对于非空有限整数集X,
,定义
,对
现有两个非空有限整数集A,B,已知
且
.
(1)当
时求集合B;
(2)证明:
;
(3)当
且
时,任取
构造函数
问:当a,b取何值时,
的最小值最小?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b18b109a656b62fb173680ae99ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9451ce4fed053674ea20d5b455b783d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb70a272d3abd0bb156e332e75dc36b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43cd3b18a04c9a72a0bf7791bdf56a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9a194c0b9152e11aabc059c8483b93.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba387b457949fde336790c9d05c4f1c.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15d281a85375fcf633d2cd86e294028.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eeee50bc500aad281fbb28d465db5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4a0f5fcd7882200fa25b6ee5143f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c41c277675b413bbff28387082c9785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbad171aea431ed7347bcdc7fbef54d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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名校
解题方法
8 . 对非空数集T,给出如下定义,
定义1:若
,
,当
时,
,则称T为强和差集;
定义2:若
,
,当
时,
,则称T为弱和差集.
(1)分别判断
是否为强和差集,
是否是弱和差集,并说明理由;
(2)若集合
是弱和差集,求A;
(3)若强和差集B的元素个数为12,且
,求满足条件的集合B的个数.
定义1:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d81972b1768d827ba3083f96a273412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760be062c0e1175db3cf059302e9893b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3866ffa03f828d57269c805c08e8c13a.png)
定义2:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d81972b1768d827ba3083f96a273412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b722d685d1c56d4d29ba137db59e25c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cf655e7150f4759685df48b605dc8f2.png)
(1)分别判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b2be1b0b6bea70d4e64894f1009359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ab4879d5e412739c7aeba46dd0ffdb.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039abfbcdcc01da76d4123f81cf0f6a5.png)
(3)若强和差集B的元素个数为12,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0d1c7c644d841c90d84dd75c562d9e.png)
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名校
解题方法
9 . 已知关于x的函数
和
.
(1)若
,求x的取值范围;
(2)若关于x的不等式
(其中
)的解集
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce81be7dbac1bd6ad7b3b6be3c2d423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28b848513cf03ef4bd4bddfd49800f6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df86b0da538701c08fb214608e062372.png)
(2)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5e74c814429bbef147280ecd517ffd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e419fd930ea3b349e70d35de4380cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e383eff7191e3bbe549027ef71382aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b3185579edda8ea518daf2be3e0d30.png)
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10 .
,满足
,且有
,
.
(1)求
,
的解析式.
(2)令
的图象位于
上方的
的取值的集合为
,有
,使
中
,且满足
的
的取值只有一对.设
所对边分别为
,其中
,
是线段
上一动点.证明:
为定值
(3)在(2)的条件下
为
内部一点,求
最小值.
注:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bd13c09822d74f612305c31ad744e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cfc436062d7dd474cb4f9c512d0a3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e603ec0775001fae01dc90c7e688d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0c1044d6a79641b2190d82a5589ce.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffa80473beb3aa3da5c377df90bfe29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efc05267f74418011231dd344514474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f8917a804e6389067077a0bebecd03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629b10e9b8c82b97a738e06277e603a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99f18b1eb117fed2b2970a3a86c083a.png)
(3)在(2)的条件下
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a00c58dd635d2a57058028777ae0bf.png)
注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737abc86a8a9f090ecc5c6f7d4424c2.png)
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