题目已知a,b为非负数,M=a4+b4,a+b=1,求M的最值.这是2006年清华大学自主招生考试中出现的题目.它有两个特征:(1)题目结构精巧,形式简洁清晰,立意新颖;(2)解题入口宽,能很好地考查学生分析问题、解决问题的能力.下面笔者从解题方法的角度进行研究、评析.方法1(对称引参) The problem is known a, b is non-negative, M = a4 + b4, a + b = 1, seeking the most value of M. This is the Tsinghua University entrance exam in 2006. It has two characteristics: (1 ) The topic is exquisite in structure, the form is concise and clear, the original intention is novel; (2) The question entrance is wide, can examine student’s ability to analyze and solve the problem very well.Following the author carries on the research and the appraisal from the angle of solution method. Symmetrical reference parameters)