2007年北京海淀区高三数学期中试题中的第8题是难得一见的一道好题,我在一个实验班的教学中对它略做改编,给出了以下一道值得深入探究的小题,在学生中反响颇大!题目已知函数f(x)=x2+ax+x12+xa+b(x∈R,且x≠0).若实数a,b使得函数y=f(x)在定义域上有零点,则a2+b2的最小值为()(A)5 The 8th question in the middle school test of the third year of mathematics in Haidian district of Beijing in 2007 was a rare topic. I modified it slightly in the teaching of an experimental class and gave the following question worthy of further investigation. The student has a good response! The topic is known as f(x)=x2+ax+x12+xa+b(x∈R, and x≠0). If the real numbers a,b make the function y=f(x) in the definition If there are zeros on the domain, the minimum value of a2+b2 is ()(A)5