已知x²-5x-1997=0,则代数式（x-2）³-（x-1）²+1／x-2的值为让我初二的智商能懂就行,重点要提出来,A,1999 B,2000 C,2001 D,2002

已知x²-5x-1997=0,则代数式（x-2）³-（x-1）²+1／x-2的值为让我初二的智商能懂就行,重点要提出来,A,1999 B,2000 C,2001 D,2002
已知x²-5x-1997=0,则代数式（x-2）³-（x-1）²+1／x-2的值为
让我初二的智商能懂就行,重点要提出来,A,1999 B,2000 C,2001 D,2002

已知x²-5x-1997=0,则代数式（x-2）³-（x-1）²+1／x-2的值为让我初二的智商能懂就行,重点要提出来,A,1999 B,2000 C,2001 D,2002
估计题目给出的括号有问题：[（x-2）³-（x-1）²+1]／(x-2)
=(x-2)²-[(x-1)²-1])/(x-2)
=(x-2)²-(x-1-1)*(x-1+1)/(x-2)
=(x-2)²-(x-2)*x/(x-2)
=(x-2)²-x
=x²-5x+4
又因为：x²-5x-1997=0,则：x²-5x＝1997,则：x²-5x+4＝1997+4＝2001
所以：代数式＝2001 选：C

∵x²-5x-1997=0
∴x^2-5x=1997
[(x-2)³-（x-1)²+1]/(x-2)
=[(x-2)³+1-（x-1)²]/(x-2)
={(x-2+1)[(x-2)^2-(x-2)+1]-(x-1)^2}/(x-2)
=[(x-1)(x^2-5x+7)-(x-1)^2]/(x-2)
...

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∵x²-5x-1997=0
∴x^2-5x=1997
[(x-2)³-（x-1)²+1]/(x-2)
=[(x-2)³+1-（x-1)²]/(x-2)
={(x-2+1)[(x-2)^2-(x-2)+1]-(x-1)^2}/(x-2)
=[(x-1)(x^2-5x+7)-(x-1)^2]/(x-2)
=(x-1)(x-2)(x-4)/(x-2)
=(x-1)(x-4)
=x^2-5x+4
=1997+4
=2001

所以选C

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