奥数之家
奥数论坛
简短留言
| 首页 | 竞赛大纲 | 优秀前辈 | 视频提示 | 专题讲座 | 论文锦集 | 综合训练 | 修身养性 | 家教平台 | 奥数论坛 |
 
The Twentieth Canadian Mathematical Olympiads
1988年第二十届加拿大数学奥林匹克
  1. For what real values of k do 1988x2 + kx + 8891 and 8891x2 + kx + 1988 have a common zero ?
  2. Given a triangle area A and perimeter p, let S be the set of all points a distance 5 or less from a point of the triangle. Find the area of S .
  3. Given n > 4 points in the plane, some of which are colored red and the rest black. No three points of the same color are collinear. Show that we can find three points of the same color, such that two of the points do not have a point of the opposite color on the segment joining them .
  4. Define two integer sequences a0, a1, a2, ... and b0, b1, b2, ... as follows. a0 = 0, a1 = 1, an+2 = 4an+1 - an, b0 = 1, b1 = 2, bn+2 = 4bn+1 - bn. Show that bn2 = 3an2 + 1 .
  5. If S is a sequence of positive integers let p(S) be the product of the members of S. Let m(S) be the arithmetic mean of p(T) for all non-empty subsets T of S. S' is formed from S by appending an additional positive integer. If m(S) = 13 and m(S') = 49, find S' .
点击此处查看相关视频讲解
在方框内输入单词或词组
建议使用:IE 6.0及以上版本浏览器。不支持 Netscape浏览器。 本站空间由北京师范大学提供
Copyright © 2005-2007 aoshoo.com All Rights Reserved 滇ICP备05000048号
MSN:shuxvecheng@hotmail.com QQ:316180036 E-mail:aoshoo@sina.com 电话:15810289082