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《中学数学月刊》在1997年第6期刊登了沈红梅的《一道好题的作用》,又在第10期刊登了田正平的《一道好题的简证》,给出了下面这道题:“若a>b>0,求证:(asinx+b)/(asinx-b)不能介于(a-b)/(a+b)与(a+b)/(a-b)之间”的四种解法,这道题如果利用定比分点公式来证将更巧妙。
The “Middle School Mathematics Monthly” published Shen Hongmei’s “The Role of a Good Question” in the 6th issue of 1997. In the 10th issue, he published Tian Zhengping’s “A Brief Testimony of a Good Question,” and gave the following question: “If a>b>0, verify that: (asinx+b)/(asinx-b) cannot be between (ab)/(a+b) and (a+b)/(ab)” This question will be more ingenious if you use the formula of the fixed score point.