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 16th Vietnam Mathematical Olympiad
1978年第十六届越南数学奥林匹克

A1. Find all three digit numbers abc such that 2(abc) = bca + cab.

A2. Find all values of the parameter m such that the equations x2 = 2|x| + |x| - y - m = 1 - y2 have only one root.

A3. The triangle ABC has angle A = 30o and AB = 3/4 AC. Find the point P inside the triangle which minimises 5 PA + 4 PB + 3 PC.

B1. Find three rational numbers a/d, b/d, c/d in their lowest terms such that they form an arithmetic progression and b/a = (a + 1)/(d + 1), c/b = (b + 1)/(d + 1).

B2. A river has a right-angle bend. Except at the bend, its banks are parallel lines a distance a apart. At the bend the river forms a square with the river flowing in across one side and out across an adjacent side. What is the longest boat of length c and negligible width which can pass through the bend ?

B3. ABCDA'B'C'D' is a rectangular parallelepiped (so that ABCD and A'B'C'D' are faces and AA', BB', CC', DD' are edges). We have AB = a, AD = b, AA' = c. The perpendicular distances of A, A', D from the line BD' are p, q, r. Show that there is a triangle with sides p, q, r. Find a relation between a, b, c and p, q, r.

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