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在根式的化简、求值运算中．若根据数字特征作灵活代换．往往使问题巧妙获解．现举例说明例1化简（1992年山东省初中教学竞赛题）例2（1992年“勤奋杯”全国数学邀请赛初二试题）解发设解设，则xy＝1.∴原式＝（x3＋y3）＋（x＋y）－（x－y）2＝（x2－xy＋y2）－（x－y）2＝xy
In the root simplification and evaluation operations. If based on digital features for flexible substitution. Often cleverly solved the problem. Now give an example to illustrate the simplification of Example 1 (Shandong Junior High School Teaching Competition in 1992). Example 2 (Introduction to the second grade of the “Diligence Cup” national mathematics invitational tournament in 1992). Solve the problem and set the solution, then xy=1. ∴Formula=(x3+y3) )+(x+y)-(x-y)2=(x2-xy+y2)-(x-y)2=xy