x+1/x=3 x＞0
(x+1/x)^2=x^2+1/x^2+2*x*1/x=x^2+1/x^2+2=9
所以x^2+1/x^2=7
(x-1/x)^2=x^2+1/x^2-2*x*1/x=7-2=5
x-1/x=±√5
x^2-1/x^2=(x+1/x)(x-1/x)=3*(±√5)=±3√5