Question

已知x平方-x-1=0,则x四次方+2x+1/x五次方=

Answer 1

x^2-x-1=0

x^2=x+1

x^4=(x+1)²=x²+2x+1=(x+1)+2x+1=3x+2

x^5=x^4*x=(3x+2)*x=3x²+2x=3(x+1)+2x=5x+3

(x^4+2x+1)/x^5

=[(3x+2)+2x+1]/(5x+3)

=(5x+3)/(5x+3)

=1