已知x^-X-1=0,则分式X4次方+2X+1/X5次方

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已知x^-X-1=0,则分式X4次方+2X+1/X5次方

已知x^-X-1=0,则分式X4次方+2X+1/X5次方
已知x^-X-1=0,则分式X4次方+2X+1/X5次方

已知x^-X-1=0,则分式X4次方+2X+1/X5次方
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