一道考研试题的多种解法与推广

Solutions and Generalizations of a Mathematical Problem

分别利用重积分化为累次积分法、轮换对称性结合先二后一法、重心坐标公式、等值面法、微元法、变量替换等方法,给出北京大学一道研究生入学试题的多种解法,并将这道试题推广为一般形式.

Using various methods such as symmetry,barycentric coordinates isosurface,and infinitesimal method,we provide nine solutions to a problem in the Graduate Admission Examination of Peking university.The general form of the problem is also discussed.