Question

已知x^2-x-1=0,求(x^4+2x +1)/x^5的ŀ

Answer 1

x^2-x-1=0,
所以x^2=x+1,
x^4=(x^2)^2=(x+1)^2=x^2+2x+1=3x+2,
x^5=x*x^4=3x^2+2x=3(x+1)+2x=5x+3,
所以(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