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文[1]作为“研究性学习”的案例从多角度给出了题目设p0,q0,p3+q3=2,求证p+q≤2的多种解法.受此启发,继续探索,现从另一角度作为“研究性学习”的案例提供于此.1现用分离变量给出一种直接的证法不妨设p≤q,于是p3≤q3,由p3+q3=2得q3-1=1-p3≥0,即(q-1)(q2+q+1)=-(p3-1)=-(p-1
The article [1] as a case of “research learning” gives a variety of solutions to the problem of p0, q0, p3+q3=2 and verification of p+q ≤ 2 from various perspectives. Inspired by this, we continue to explore. Another perspective is provided as a case of “research learning”. 1 The current segregation variable gives a direct proof that p ≤ q, then p3 ≤ q3, and p3 + q3 = 2 gives q 3-1 = 1-p3 ≥ 0, that is (q-1)(q2+q+1)=-(p3-1)=-(p-1