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六年制重点中学《代数》第二册上,有这样一道题(见P、110练习七第11题):“求证|x+1/x1≥2,x≠0”,这个命题告诉我们这样一个事实:只要x是非零实数,那么|x+1/x|≥2。既然这个命题正确,那么它的逆否命题:“如果|x+1/x|<2,则x不是实数”,也自然就正确了。对于x+1/x=2cosθ来说,显然满足|x+1/x|=2|cosθ|≤2,等号在θ=kπ时成立,因此,只要θ≠kπ,那么x+1/x=2cosθ中的x就一定不是实数了。
In the second grade of the six-year key middle school “Algebra”, there is such a question (see P, 110, Exercise 7, Item 11): “Prove|x+1/x1≥2, x≠0”, this proposition tells us that A fact: As long as x is a non-zero real number, then |x+1/x|≥2. Since this proposition is correct, then its inverse proposition: “If |x+1/x|<2, then x is not a real number”, it is naturally correct. For x+1/x=2cosθ, it is obvious that |x+1/x|=2|cosθ|≤2, and the equal sign holds at θ=kπ. Therefore, as long as θ≠kπ, then x+1/x The x in =2cosθ must not be a real number.