命题试证对任意a、b∈R,有max{|a+b|,|a-b|,|1-b|}≥21.分析(1)题目含义:在题设条件下,要证明|a+b|,|a-b|,|1-b|三者之中的最大数不小于21,由于a、b取值的任意性,即是要证明三者之中至少有一个不小于21.因此可以得到.(2)证题思路①若假设三者均小于12,则必有矛盾;②若假设三者 Proposition test for any a, b ∈ R, there is max{|a+b|,|ab|,|1-b|} 21. Analysis (1) The meaning of the topic: Under the conditions of the problem, to prove |a The maximum number among +b|,|ab|,|1-b| is not less than 21. Because of the arbitrariness of a and b, it is necessary to prove that at least one of the three is not less than 21. Can be obtained. (2) Testimony Idea 1 If we assume that all three are less than 12, there must be a contradiction; 2 if three are assumed