已知A是X^2-X-1=0的一个根,所以A^2-A-1=0,变形得:A^2=A+1
2009-A^3+2A^2
=2009-A^2(A-2) 将A^2=A+1代入
=2009-(A+1)(A-2)
=2009-(A^2+A-2A-2)
=2009-(A^2-A-2)将A^2=A+1代入
=2009-(A+1-A-2)
=2009+1
=2010
完毕!
已知A是X^2-X-1=0的一个根,所以A^2-A-1=0,变形得:A^2=A+1
2009-A^3+2A^2
=2009-A^2(A-2) 将A^2=A+1代入
=2009-(A+1)(A-2)
=2009-(A^2+A-2A-2)
=2009-(A^2-A-2)将A^2=A+1代入
=2009-(A+1-A-2)
=2009+1
=2010
完毕!