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在某本中学数学习题选解中,有题目与解答如下: 问题1:求函数y=2cos~2x-3cosx+1的极小值。解:∵2cos~2x-3cosx+(1-y)=0 由cosx取实数,其判别式须 b~2-4ac=9-4×2(1-y)≥0 ∴y≥-1/8 即函数的极小值是-1/8。从表面上看,这题的解法是比较简便的,且结果也是正确的。然而,这种解题方法是否正确呢?我认为是值得商榷的。现已发现有些学生仿此法求解类似问题而导致错
In the selection of a certain number of middle school mathematics questions, there are questions and answers as follows: Question 1: Find the minimum value of the function y=2cos~2x-3cosx+1. Solution: ∵2cos~2x-3cosx+(1-y)=0 Take a real number from cosx. The discriminant must be b~2-4ac=9-4x2(1-y)≥0 ∴y≥-1/8. The minimum value of the function is -1/8. On the surface, the solution to this problem is relatively simple and the result is correct. However, is this method of solving problems correct? I think it is debatable. Some students have found that this method causes similar mistakes