已知x²-5x-1997=0,求代数式[（x-2）³-（x-1）²+1]/(x-2)

题目

已知x²-5x-1997=0,求代数式[（x-2）³-（x-1）²+1]/(x-2)

答案

∵x²-5x-1997=0∴x²=5x+1997∴[(x-2)³-(x－1)²＋1]/(x-2)=(x-2)²-[(x-1)²-1]/(x-2)又(x-2)²=x²-4x+4=5x+1997-4x+4=x+2001(x-1)²-1=x²-2x=5x+1997-2x=3x+1997∴原...