美国著名数学教育学家波利亚说:“一个专心的认真备课的教师能够拿出一个有意义的但又不复杂的题目.去帮助学生挖掘问题的各个方面,使得通过这道题,就好像通过一道门户,把学生引入一个完整的理论领域.”本文通过对一个问题的多解谈谈合理选择思路,提高解题效率的一些感想.问题已知正数a,b满足2a~2+b~2=3,则 Polly, a famous American mathematical educator, said: “A dedicated lesson preparation teacher can come up with a meaningful but uncomplicated topic to help students tap all aspects of the problem, so that through this question, Seems through a portal, the students into a complete field of theory. ”This article by a multi-solution to a question to talk about the rational choice of thinking, to improve the efficiency of some problems. The problem is known positive a, b satisfy 2a ~ 2 + b ~ 2 = 3, then