已知：m-1/m=3,则(m^3)-1/(m^3)=____

题目

已知：m-1/m=3,则(m^3)-1/(m^3)=____
求值

答案

(m^3)-1/(m^3)
=(m-1/m)(m^2+m*1/m+1/m^2)
=(m-1/m)(m^2+1+1/m^2)
=(m-1/m)(m^2-2+1/m^2+3)
=(m-1/m)[(m-1/m)^2+3)
=3*(3^2+3)
=36