已知x^2+x-1=0,求代数式2x^4+5x^3

已知x^2+x-1=0,求代数式2x^4+5x^3-4x^2-8x+2014的值

1个回答

2x^4+5x^3-4x^2-8x+2014
=2x^4+2x^3-2x^2+3x^3+3x^2-3x-5x^2-5x+5+2009
=2x^2(x^2+x-1)+3x(x^2+x-1)-5(x^2+x-1)+2009
=2x^2*0+3x*0-5*0+2009
=2009