1值得商榷的“范围”问题的求解文[1]对中学数学中常见问题“求变量的范围”的理解具有颠覆性,让人耳目一新,振人发聩.但细品之后,文中观点也是值得商榷的.现将文中主要观点及论述过程摘录如下:“问题1设m,n∈R,若直线(m+1)x+(n+1)y-2=0与圆(x-1)2+(y-1)2=1相切,则m+n的取值范围是()A.[1-3,1+3]B.(-∞,1-3]∪[1+3,+∞)C.[2-2 2,2+2]D.(-∞,2-2]∪[2+2 2,+∞) A questionable solution to the ”range“ problem [1] is disruptive to common problems in high school mathematics, and ”the scope of variables", which makes people refreshing and refreshing .But after the fine, The point of view in this paper is also debatable. Now, the main points of the paper and the exposition process are excerpted as follows: Problem 1 Let m, n∈R, if the line (m + 1) x + (n + 1) (-1) 2 + 1, then the range of m + n is () A. [1-3,1 + 3] B. (- ∞, 1-3] ∪ [1 + 3, + ∞) C. [2-2 2,2 + 2] D. (- ∞, 2-2] ∪ [2 + 2 2, + ∞)