已知x^2-x-1=0,则-x^3+2x^2+2008=?

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已知x^2-x-1=0,则-x^3+2x^2+2008=?已知x^2-x-1=0,则-x^3+2x^2+2008=?已知x^2-x-1=0,则-x^3+2x^2+2008=?x^2-x-1=0x

已知x^2-x-1=0,则-x^3+2x^2+2008=?
已知x^2-x-1=0,则-x^3+2x^2+2008=?

已知x^2-x-1=0,则-x^3+2x^2+2008=?
x^2-x-1=0
x²-x=1
-x^3+2x^2+2008=
= -x³+x²+x²+2008
= -x(x²-x)+x²+2008
= -x +x²+2008
=1+2008
=2009

-x^3+2x^2+2008
=-x(x+1)+2(x+1)+2008
=-x²-x+2x+2+2008
=-x²+x+2010
=-(x²-x)+2010
=-1+2010
=2009

∵x^2-x-1=0
∴x^3-x^2-x=0
-x^3+x^2+x=0
∴-x^3+2x^2+2008
=(-x^3+x^2+x)+x^2-x-1+2009
=0+0+2009
=2009

已知: x^2-x-1=0
-x^3+2x^2+2008
=-x^3+x^2+X+x^2-X+2008
=-(x^3-x^2-X)+x^2-X-1+2009
=-x(x^2-x-1)+(x^2-x-1)+2009
=x*0+0+2009
=2009