已知x^2+x-1=0,则x^4-x^3+2x^2

已知x^2+x-1=0,则x^4-x^3+2x^2+7x+2000=____ x^5+x^4-3x^3-2x^2+2x+

1个回答

x^2+x=1
x^4-x^3+2x^2+7x+2000=x^2(x^2+x)-x^3-x^3+2x^2+7x+2000
=x^2-2x^3+2x^2+7x+2000=-2x(x^2+x)+2x^2+3x^2+7x+2000
=5x^2+5x+2000=2005
同样道理去换,得到二式=4