a^3+1/(a^3)=(a+1/a)(a^2-1+1/(a^2))
而（a+1/a）^2=3,整理得a^2+1/(a^2)=1
所以a^3+1/(a^3)=(a+1/a)(a^2-1+1/(a^2))=（a+1/a）（1-1）=0