1 . 已知等比数列
的公比为q,求证:对于任意的正整数m,n,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16dc6ca1848862dc2871623c3a49ef7a.png)
您最近一年使用:0次
2 . 利用十字相乘法分解因式:
(1)
;
(2)
.
(3)求方程
的解集.
(4)求证:对任意的x,a,b,都有
.
(5)已知“任意l和s,都有
”是真命题,借助这个结论将
进行因式分解.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdf57778bfe4dab4ee539f27ec9758c.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96791c33798bd64168fbcfed8227e3d7.png)
(3)求方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86eb4ca4061cc0763ceb703feebc2b69.png)
(4)求证:对任意的x,a,b,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a22f618009ca40d3c793a14fdbf1b32d.png)
(5)已知“任意l和s,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84b242ba1b490d6179e5f68f425bcd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ac4ca64fdb94ebfac63b6d45a453be.png)
您最近一年使用:0次
3 . 已知函数
,设数列
的通项公式为
,其中
;
(1)求证:
;
(2)判断
是递增数列还是递减数列,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257c354288473ba96653349e3877c44e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c58e99e3c3a921cd712906b0a3b1091d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe977dbfe794d737902609918f4dec63.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d160d0c1845e37390c487cffb4f00ce3.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
解题方法
4 . (1)已知
,
,求证:
;
(2)已知
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1acb490f64af2e29776c84ea50fd33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7be8524456ba4e9abb973da323c0c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c7df8168b488d16fa7292a594e9424.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d89ab55ffb93cc48f077b542dbd25aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13c26fb693648f35f44b06b042029aa.png)
您最近一年使用:0次
解题方法
5 . 设R是
的外接圆的半径,S是
的面积,求证:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0012d80fbc83bec6323b11aea42655.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67197ecaecaecbe3590f75d35998d64a.png)
您最近一年使用:0次
6 . 如图,已知AM是
中BC边上的中线.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b73d9d332018afea17a39cb7aee142.png)
您最近一年使用:0次
7 . 对任意三个正实数
,
,
,求证:
,当且仅当
时等号成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef3052cd1be7641eb559c5d7ed142cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44acc0ee22dc4b7750e8be825e7c1355.png)
您最近一年使用:0次
8 . 设a,b为正数,证明下列不等式成立:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa23408bcc9f6200f22a310e5f2569a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7efecdd67f1088510886e88b80263bd8.png)
您最近一年使用:0次
解题方法
9 . 设
,
,求证下列不等式:
(1)
;
(2)
;
(3)
;
(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216682504182873f78cc43e6e46799cb.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0274fb77878866cc088d719a060e3f.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d2e0a4dc2e7a7e72c1620374e038b8.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9fc73d3810e2573cfc02488c41baab.png)
您最近一年使用:0次
10 . 求证:如果
,且
,那么
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce9bd1c1a6eff394f373b89e1720ff8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0dfded1758cbd9a49da73deaa741609.png)
您最近一年使用:0次