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不久前我校模拟了2015年台州市高三第一学期期末统考试卷,试卷的第15题以二次方程有根为命题背景,试题虽短小精悍,但出现了多个变量,给很多学生造成了思维障碍.经过老师详细分析,结合自己的失误成因,再反复思考,我发现它是一道很有韵味的试题,解法多样,蕴含多种数学思想方法,可以放飞我们的解题思维.题目若关于x的方程x~2+ax+1/x~2+a/x+b=0有实根,则a~2+b~2的最小值为__.
Not long ago, our school simulated the final exam paper for the first semester of the third year of Taizhou in 2015. The 15th item in the paper takes the root of the quadratic equation as the proposition background. Although the exam questions are short and concise, there are many variables that have caused many students thinking Obstacles.After a detailed analysis of the teacher, combined with their own causes of mistakes, and then repeatedly thinking, I found it is a very interesting questions, solutions and diverse, contains a variety of mathematical ideas and methods that can fly our problem-solving thinking. The equation x2 + ax + 1 / x ~ 2 + a / x + b = 0 has a real root, then the minimum value of a ~ 2 + b ~ 2 is __.