设X^(1/6)=Y,方程可化简为:Y^3-3Y^2=3Y-9,移项得Y^3-3Y^2-3Y+9=0,Y^2(Y-3)-3(Y-3)=0,(Y^2-3)(Y-3)=0,(Y-根号3)(Y+根号3)(Y-3)=0,则Y有3个根号3,-根号3,3,即X^(1/6)=根号3或-根号3或3,解得X=27(当X^(1/6)=根号3或-根号3时解得的X相同)或729.
设X^(1/6)=Y,方程可化简为:Y^3-3Y^2=3Y-9,移项得Y^3-3Y^2-3Y+9=0,Y^2(Y-3)-3(Y-3)=0,(Y^2-3)(Y-3)=0,(Y-根号3)(Y+根号3)(Y-3)=0,则Y有3个根号3,-根号3,3,即X^(1/6)=根号3或-根号3或3,解得X=27(当X^(1/6)=根号3或-根号3时解得的X相同)或729.