a: \(A=\sqrt[3]{10-6\sqrt{3}}+\sqrt[3]{10+6\sqrt{3}}\)
=>\(A^3=10-6\sqrt{3}+10+6\sqrt{3}+3\cdot\sqrt[3]{\left(10-6\sqrt{3}\right)\left(10+6\sqrt{3}\right)}\cdot\left(\sqrt[3]{10+6\sqrt{3}}+\sqrt[3]{10-6\sqrt{3}}\right)\)
=>\(A^3=20+3\cdot\left(-2\right)\cdot A\)
=>\(A^3+6A-20=0\)
=>\(A^3-2A^2+2A^2-4A+10A-20=0\)
=>\(\left(A-2\right)\left(A^2+2A+10\right)=0\)
=>A-2=0
=>A=2
=>A là số nguyên
b: \(B=\sqrt[3]{9+4\sqrt{5}}+\sqrt[3]{9-4\sqrt{5}}\)
=>\(B^3=9+4\sqrt{5}+9-4\sqrt{5}+3\cdot\sqrt[3]{\left(9+4\sqrt{5}\right)\left(9-4\sqrt{5}\right)}\cdot\left(\sqrt[3]{9+4\sqrt{5}}+\sqrt[3]{9-4\sqrt{5}}\right)\)
=>\(B^3=18+3B\)
=>\(B^3-3B-18=0\)
=>\(B^3-3B^2+3B^2-9B+6B-18=0\)
=>\(\left(B-3\right)\left(B^2+3B+6\right)=0\)
=>B-3=0
=>B=3
=>B là số nguyên
