设a=(2+√5)^(1/3)b=(2-√5)^(1/3)则a^3+b^3=4a^3+b^3=(a+b)(a^2-ab+b^2)=4a^2+b^2=(a+b)^2-2abab=(2+√5)^(1/3)*(2-√5)^(1/3)=[(2+√5)(2+√5)]^(1/3)=(4-5)^(1/3)=-1所以a^2+b^2=(a+b)^2+2所以(a+b)[(a+b)^2-3ab]...