已知X的值满足式子X^2+X-1=0,求2008X^3+4016X^2的值

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已知X的值满足式子X^2+X-1=0,求2008X^3+4016X^2的值
已知X的值满足式子X^2+X-1=0,求2008X^3+4016X^2的值

已知X的值满足式子X^2+X-1=0,求2008X^3+4016X^2的值
x^2+x=1
2008x^3+4016x^2
=2008x^3+2008x^2+2008x^2
=2008x(x^2+x)+2008x^2
=2008x*1+2008x^2
=2008(x^2+x)
=2008

2008x^3+4016x^2=2008x^2(x+2)=2008(1-x)(x+2)
=2008(x-x^2+2-2x)=2008(-x^2-x+2)=2008(-1+2)=2008