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 20th Vietnam Mathematical Olympiad 1982年第20届越南奥林匹克数学竞赛 A1.　Find a quadratic with integer coefficients whose roots are cos 72o and cos 144o. A2.　Find all real solutions to x(x + 1)(x + 2)(x + 3) = m - 1. A3.　ABC is a triangle. A' is on the same side of BC as A, and A" is on the opposite side of BC. A'BC and A"BC are equilateral. B', B", C', C" are defined similarly. Show that area ABC + area A'B'C' = area A"B"C". B1.　Find all positive integer solutions to 2a + 2b + 2c = 2336. B2.　n is a positive integer. x and y are reals such that 0 ≤ x ≤ 1 and x n+1 ≤ y ≤ 1. Show that the absolute value of (y - x)(y - x2)(y - x3) ... (y - xn )(1 + x)(1 + x2) ... (1 + xn ) is at most (y + x)(y + x2) ... (y + xn )(1 - x)(1 - x2) ... (1 - xn ). B3.　ABCDA'B'C'D' is a cube (ABCD and A'B'C'D' are faces and AA', BB', CC', DD' are edges). L is the line joining the midpoints of BB' and DD'. Show that there is no line which meets L and the lines AA', BC and C'D'. 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