Trả lời:
\(E=\sqrt[3]{\sqrt{5}-2}+\sqrt[3]{\sqrt{5}+2}\)
\(2E=2.\sqrt[3]{\sqrt{5}-2}+2.\sqrt[3]{\sqrt{5}+2}\)
\(2E=\sqrt[3]{8\sqrt{5}-16}+\sqrt[3]{8\sqrt{5}+16}\)
\(2E=\sqrt[3]{5\sqrt{5}-15+3\sqrt{5}-1}+\sqrt[3]{5\sqrt{5}+15+3\sqrt{5}+1}\)
\(2E=\sqrt[3]{\left(\sqrt{5}-1\right)^3}+\sqrt[3]{\left(\sqrt{5}+1\right)^3}\)
\(2E=\sqrt{5}-1+\sqrt{5}+1\)
\(2E=2\sqrt{5}\)
\(E=\sqrt{5}\)
\(F=\sqrt[3]{182+\sqrt{33125}}+\sqrt[3]{182-\sqrt{33125}}\)
\(F=\sqrt[3]{182+25\sqrt{53}}+\sqrt[3]{182-25\sqrt{53}}\)
\(2F=2.\sqrt[3]{182+25\sqrt{53}}+2.\sqrt[3]{182-25\sqrt{53}}\)
\(2F=\sqrt[3]{1456+200\sqrt{53}}+\sqrt[3]{1456-200\sqrt{53}}\)
\(2F=\sqrt[3]{343+147\sqrt{53}+1113+53\sqrt{53}}+\sqrt[3]{343-147\sqrt{53}+1113-53\sqrt{53}}\)
\(2F=\sqrt[3]{\left(7+\sqrt{53}\right)^3}+\sqrt[3]{\left(7-\sqrt{53}\right)^3}\)
\(2F=7+\sqrt{53}+7-\sqrt{53}\)
\(2F=14\)
\(F=7\)
