本文给出代数式求值的几种常见模型 ,如果能将所给问题中的代数式归结为下述模型 ,便可以快速求值 .模型 1　化成x+1x =a例 1　已知x +1x =2 ,那么xx2 +3x+1 -xx2 +9x+1 的值等于.( 2 0 0 1年河北省初中数学创新与知识应用竞赛试题 )解　将x +1x =2两边平方并整理得x+1x =2 ,则 In this paper, several common models for algebraic expression evaluation are given. If algebraic expressions in the given problem can be reduced to the following models, they can be quickly evaluated. Model 1 is transformed into x+1x = a case 1 Known x +1x = 2 Then, the value of xx2 +3x+1 -xx2 +9x+1 is equal to. (The Hebei provincial junior high school mathematics innovation and knowledge application contest questions in the year of 2001) Solution Solve the x +1x = 2 sides and arrange it to get x+1x = 2 , then