x²-x-1=0,﹙x∧4+2x+1﹚/x²=
∵x²-x-1=0 ,∴x1=(1+√5)/2 ,x2=(1-√5)/2.x²=x+1.
﹙x∧4+2x+1﹚/x²=x²+2/x+1/x²=x+1+2/x+1/﹙x+1﹚
若x=(1+√5)/2 ,原式=(1+√5)/2+1+2/[(1+√5)/2]+1/[(1+√5)/2+1]=2+√5.
若x=(1-√5)/2 ,原式=(1-√5)/2+1+2/[(1-√5)/2]+1/[(1-√5)/2+1]=2+√5.
∴﹙x∧4+2x+1﹚/x²=2+√5.
——贤子.