已知X^2-5X-1999=0,求代数式(X-2)^3-(X-1)^2+1/(X-2)

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已知X^2-5X-1999=0,求代数式(X-2)^3-(X-1)^2+1/(X-2)已知X^2-5X-1999=0,求代数式(X-2)^3-(X-1)^2+1/(X-2)已知X^2-5X-1999=

已知X^2-5X-1999=0,求代数式(X-2)^3-(X-1)^2+1/(X-2)
已知X^2-5X-1999=0,求代数式(X-2)^3-(X-1)^2+1/(X-2)

已知X^2-5X-1999=0,求代数式(X-2)^3-(X-1)^2+1/(X-2)
因为X^2-5X-1999=0,即X^2-5X=1999
所以
[(X-2)^3-(X-1)^2+1]/(X-2)=(x-2)^2-(x^2-2x+1)/(x-2)+1/(x-2)
=(x-2)^2-(x^2-2x)/(x-2)-1/(x-2)+1/(x-2)
=x^2-4x+4-x-1/(x-2)+1/(x-2)
=x^2-5x+4
=1999+4
=2003