名校
解题方法
1 . 希罗平均数(Heronianmean)是两个非负实数的一种平均,设
是两个非负实数,则它们的希罗平均数
关于希罗平均数有如下说法:
①若
则
的希罗平均数
;
②三棱台
的体积
恰好是以此三棱台的上、下底面为底面且与此三棱台等高的两个三棱柱的体积
的希罗平均数;
③已知等差数列
和等比数列
的首项均为1,且
记
为
与
的希罗平均数,则数列
的前
项和
;
④在直角
中,
,则
的希罗平均数的取值范围为
;
⑤已知正四棱锥
的底面
的内切圆
的半径为
(点
为内切圆圆心),记
若
则正四棱锥
的外接球的半径
不小于
的希罗平均数.
其中正确的有___________ (填写所有正确结论的编号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a7a0726a3ac33110c3637cd92674ea.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34c590f48c84fe471d1af522c343c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ac66fed87aa83f39c224878d1e0c06.png)
②三棱台
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46bd37096f7014e00fd079823b6c3c3.png)
③已知等差数列
![](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/cbb017288d4b656a5a115794355924f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a466b9a1a8bc7a50484702d326d124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc99d52c4d23ea20f480a68b82b23298.png)
④在直角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b85155ef02a3d4ad84819e14d0c12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c870ef83e4e9eb140594ffdd7f5600a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41003e232db74364578d50366c2d379.png)
⑤已知正四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bac3d1a04dda98a6a11508d3372b020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e1d6c40c29815018e07d861f5a78cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1960fa68fec9bbf4779e70c80de02d0d.png)
其中正确的有
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