若x²+x-2=0,则x³+2x²-x+2007=

若x²+x-2=0,则x³+2x²-x+2007=
若x²+x-2=0,则x³+2x²-x+2007=

若x²+x-2=0,则x³+2x²-x+2007=
x²+x-2=0
（x-1）（x+2）=0
x=1或x=-2
当x=1时 x³+2x²-x+2007=1+2-1+2007=2009
当x=-2时x³+2x²-x+2007=-8+8+2+2007=2009
综上x³+2x²-x+2007=2009

x²+x-2=0
x²+x=2
x³+2x²-x+2007
=x(x²+x)+x²-x+2007
=2x+x²-x+2007
=x²+x+2007
=2+2007
=2009

2009

由已知有x³+x²-2x=0
故所求式=x³+x²-2x+x²+x+2007=0+2+2007=2009

x³+2x²-x+2007=x(x²+x-2)-x²+2x+2x²-x+2007=(x+1)(x²+x-2)+2009=0×(x+1)+2009=0+2009=2009