令a=x+1/x则a²=x²+2+1/x²x²+1/x²=a²-2所以a²-2-3a+4=0a²-3a+2=(a-1)(a-2)=0a=1,a=2x+1/x=1两边乘xx²-x+1=0判别式小于0，无解x+1/x=2x²-2x+1=0(x-1)²=0x=1综上x=1
