已知x²-5x-2007=0,求(x-2)分之(x-2)³-(x-1)²+1的值

已知x²-5x-2007=0,求(x-2)分之(x-2)³-(x-1)²+1的值
已知x²-5x-2007=0,求(x-2)分之(x-2)³-(x-1)²+1的值

已知x²-5x-2007=0,求(x-2)分之(x-2)³-(x-1)²+1的值
(x-2)分之(x-2)³-(x-1)²+1
原式=(x-2)²-[(x-1)²-1]／(x-2)
=(x-2)²-(x²-2x)／(x-2)
=(x-2)²-[x(x-2)]/(x-2)
=(x-2)²-x
=x²-4x+4-x
=x²-5x+4
∵x²-5x-2007=0
∴x²-5x=2007
∴x²-5x+4=2007+4=2011

[(x-2)³-(x-1)²+1]/(x-2)
=[(x-2)³-(x-1+1)(x-1-1)]/(x-2)
=(x-2)²-x
=x²-5x+4
=x²-5x-2007+2011
=2011

[(x-2)³-(x-1)²+1]/(x-2)
=[(x-2)³-(x-1+1)(x-1-1)]/(x-2)
=[(x-2)³-x(x-2)]/(x-2)
=(x-2)²-x
=x²-5x+4
x²-5x-2007=0 x²-5x=2007
即 x²-5x+4=2011