∵x^2-x-1=0,∴x^2=x+1,x=(1±√5）/2,1/x=(-1±√5）/2
x^4+1/x^4=(x^2-1/x^2)^2+2=[(x^4-1)/x^2]^2=[(x^2+1)(x^2-1)/x^2]^2=[(x+2)x/x^2]^2=(1+2/x)^2=5