题目对于任意实数a,b,不等式max{|a+b|,|a-b|,|2012-a|}≥c恒成立,求常数c的最大值.(注:max{x,y,z}表示x,y,z中的最大者)这是2011年世界数学团体锦标赛青年组团体赛第3题,题中涉及x,y,z中的最大者的符号表示max{x,y,z},同样的我们习惯地用min{x,y,z}表示x,y,z中的最小者.从整体上看,这是一道不等式恒成立问题,我们可以将其转化为最值问题: The problem for any real a, b, inequality max {| a + b |, | ab |, | 2012-a |} ≥ c constant holds, the maximum value of the constant c (Note: max {x, y, z} Which means the largest of x, y, z) This is Question 3 of the World Series of Mathematic Group Championships 2011, with the symbols involving the largest of x, y, and z representing max {x, y, z} Similarly, we use min {x, y, z} to denote the smallest of x, y, z.On the whole, this is an inequality that holds, and we can transform it into the most value problem: