Question

已知x^2-x-1=0,求(x^4+2x +1)/x^5的值

Answer 1

x²-x-1=0
x²=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

Answer 2

x²-x-1=0
x+1=x²
(x^4+2x+1)/x^5
=(x^4+x+x+1)/x^5
=(x^4+x²+x)/x^5
=(x^3+x+1)/x^4
=(x^3+x²)/x^4
=(x+1)/x²
=x²/x²
=1