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题目已知p>0,q>0,且p~3+q~3=2,求证:p+q≤2.这是1986年江苏省宿州市初中数学竞赛题.稍作改动,成为1988年江苏省初中数学竞赛题:已知p3+q3=2,其中p,q都是实数,试求p+q的最大值.1993年,该题又成为北京市高一数学竞赛题:x,y为实数且x~3+y~3=2,求x+y的取值范围.此题文字简洁,结构优美,设计精巧,内涵丰富,解法多样,赏心悦目.是一道很值得探究的好题.以下几种证法,在此与读者共享.
Subject known p> 0, q> 0, and p ~ 3 + q ~ 3 = 2, verify: p + q ≤ 2. This is 1986 Suzhou City, Jiangsu Province junior high school math contest title. Jiangsu Province Junior High School Math Contest Title: Known p3 + q3 = 2, where p, q are real numbers, try to find the maximum p + q. 1993, the title has become the Beijing high school mathematics competition questions: x, y For the real number and x ~ 3 + y ~ 3 = 2, find the value range of x + y.This topic is simple, beautiful structure, exquisite design, rich in content, solution is diverse, pleasing to the eye. The following kinds of card law, in this and readers to share.