ta có\(\sqrt[3]{8+3\sqrt{21}}\)+\(\sqrt[3]{8-3\sqrt{21}}\)=A 

=> A3=8+3\(\sqrt{21}\)+8-3\(\sqrt{21}\)+3\(\sqrt[3]{\left(8+3\sqrt{21}\right)\left(8-3\sqrt{21}\right)}\).A

=> A3=16+3\(\sqrt[3]{64-189}\).A

=> A3=16+3.(-5).A

=> A3=16-15A

=> A3+15A -16=0

=> A3-A2+A2-A+16A-16=0

=>A2(A-1)+A(A-1)+16(A-1)=0

=>(A-1)(A2+A+16)=0

=> A-1 =0 hoặc A2+A+16=0(vô lí vì A2+A+1/4≥0)

=> A =1 

Vậy A=1