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2016年高考数学全国乙卷理科第21题:已知函数f(x)=(1-2)e~x+a(x-1)~2有两个零点。(Ⅰ)求a的取值范围;(Ⅱ)设:x_1,x_2是f(x)的两个零点,证明:x_1+x_2<2。此题第(Ⅱ)问,很多杂志给出各种解答,称此问题为极值点解问题。文献[1]、[2]、[3]均对类似的问题给出了不同的处理策略。特别地,文献[1]给出了如下处理策略:
2016 college entrance examination Mathematics National Science Volume 21 Subject: Known function f (x) = (1-2) e ~ x + a (x-1) ~ 2 has two zero points. (Ⅰ) Find the range of a; (Ⅱ) Let x1 and x_2 be two zero points of f (x), and prove that: x_1 + x_2 <2. Question (II) asked many magazines to give a variety of answers, saying that the problem is the extreme solution. References [1], [2], [3] all give different treatment strategies for similar problems. In particular, [1] gives the following treatment strategies: