已知x2+x-1=0,求x3-2x+2009的值

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已知x2+x-1=0,求x3-2x+2009的值
已知x2+x-1=0,求x3-2x+2009的值

已知x2+x-1=0,求x3-2x+2009的值
x²+x-1=0
∴x²+x=1
x³-2x+2009
=x³+x²-x²-x-x+2009
=x(x²+x)-(x²+x)-x+2009
=x-1-x+2009
=2008

x²+x-1=0,
x²+x=1
x³-2x+2009
=x(x²+x)-x²-2x+2009
=x-x²-2x+2009
=-(x²+x)+2009
=-1+2009
=2008

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