已知：m+1/m=3
两边平方m^2+2+1/m^2=9,m^2+1/m^2=7
(m-1/m)^2=m^2-2+1/m^2=7-2=5
m-1/m=±√5
m^2-1/m^2=(m+1/m)(m-1/m)=3(m-1/m)＝±3√5
楼主的答案是正解.