∵X^2-5X-2004=0
∴[(X-2)³-(X-1)²+1]/(X-2)+1
=[(X-2)³-(X-2+1)²+1]/(X-2)+1
=[(X-2)³-(X-2)²-2(x-2)]/(X-2)+1
=(x-2)²-(x-2)-2+1
=x²-4x+4-x+2-2+1
=x²-5x+4+1
=x²-5x-2004+2009
=2009
∵X^2-5X-2004=0
∴[(X-2)³-(X-1)²+1]/(X-2)+1
=[(X-2)³-(X-2+1)²+1]/(X-2)+1
=[(X-2)³-(X-2)²-2(x-2)]/(X-2)+1
=(x-2)²-(x-2)-2+1
=x²-4x+4-x+2-2+1
=x²-5x+4+1
=x²-5x-2004+2009
=2009