x²-5x-1=0两边同除x,得：x-5-1/x=0即：x-1/x=5(x-1/x)²=x²-2+1/x²=25则：x²+1/x²=27；(x+1/x)²=x²+2+1/x²=29所以：x+1/x=±√29元旦愉快!