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偶翻北京市高等学校招生办公室所编《一九八三年全国高等学校统一招生试题答案汇编》,见理工农医类数学试题第九题及其解答,悟出一新证法,似较原证法简便,兹录于后。原题共两个小题: 1)已知a,b为实数,并且eb~a。 2)如果正实数a,b满足a~b=b~a,且a<1,证明a=b。题1)通过考察函数y=lnx/x,或利用导数证明其在(e,+∞)内单调递减,或在[a,b]上
If you even edit the “Resolution Compilation of the National Unified Enrollment Questions for Higher Education in 1983” edited by the Admissions Office of the Beijing Higher Education Institution, see the ninth questions and answers for the Mathematics exam for agronomy and medicine and realize a new certification method. The evidence is simple and it is recorded later. There are two small questions in the original question: 1) Know that a and b are real numbers and eb~a. 2) If the positive real numbers a, b satisfy a~b=b~a and a<1, prove a=b. Question 1) By examining the function y=lnx/x, or using a derivative to prove that it is monotonically decreasing in (e,+∞), or on [a,b]