已知x²-5x-2007=0,求(x-2)分之(x-2)³-(x-1)²+1的值
问题描述:
已知x²-5x-2007=0,求(x-2)分之(x-2)³-(x-1)²+1的值
答
[(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
答
[(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
答
(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∴x...