∵x²-5x-1997=0
∴x²-5x=1997
[（x-2）^3-（x-1）²+1]/（x-2）
=(x³-6x²+12x-8-x²+2x-1+1)/(x-2)
=(x³-7x²+14x-8)/(x-2)
=(x³-8)-(7x²-14x)/(x-2)
=[(x-2)(x²+2x+4)-7x(x-2)]/(x-2)
=(x-2)(x²+2x-7x+4)/（x-2)
=x²-5x+4
=1997+4
=2001