2解析：x²+1/x²-x-1/x=0(x+1/x)²-2-x-1/x=0(x+1/x-2)(x+1/x+1)=0x+1/x=2或-1检验x+1/x=2，解得x=1x+1/x=-1x²+x+1=0(x+1/2)²+3/4=0无解故，x+1/x=-1舍去∴ x+1/x=2
