Question

Answer 1

\(A=\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}\)

\(\Rightarrow2A=2\sqrt[3]{2+\sqrt{5}}+2\sqrt[3]{2-\sqrt{5}}=\sqrt[3]{16+8\sqrt{5}}+\sqrt[3]{16-8\sqrt{5}}\)

\(\sqrt[3]{\left(\sqrt{5}+1\right)^3}+\sqrt[3]{\left(1-\sqrt{5}\right)^3}=\sqrt{5}+1+1-\sqrt{5}=2\)

\(\Rightarrow A=1\)