令x+1/x=tx²+1/x²=t²-22（x^2+1/x^2)-3(x+1/x)=12(t²-2)-3t=12t²-4-3t-1=02t²-3t-5=0(2t+2)(t-5/2)=0t=-1 舍去 ∵x²+1/x²≥0 ∴t²-2≥0t=5/2当t=5/2时 x+1/x=5/2 解得x=2 或x=-1/2望采纳
