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
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![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](/uploads/image/z/767759-23-9.jpg?t=%E5%B7%B2%E7%9F%A5x%26%23178%3B-5x-1997%3D0%2C%E5%88%99%E4%BB%A3%E6%95%B0%E5%BC%8F%EF%BC%88x-2%EF%BC%89%26%23179%3B-%EF%BC%88x-1%EF%BC%89%26%23178%3B%2B1%EF%BC%8Fx-2%E7%9A%84%E5%80%BC%E4%B8%BA%E8%AE%A9%E6%88%91%E5%88%9D%E4%BA%8C%E7%9A%84%E6%99%BA%E5%95%86%E8%83%BD%E6%87%82%E5%B0%B1%E8%A1%8C%2C%E9%87%8D%E7%82%B9%E8%A6%81%E6%8F%90%E5%87%BA%E6%9D%A5%2CA%2C1999+B%2C2000+C%2C2001+D%2C2002)
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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