Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
e.{E^3} = 2\sqrt 5 + 3\left( {\sqrt[3]{{\left( {\sqrt 5 - 2} \right)\left( {\sqrt 5 + 2} \right)}}} \right)\left( {\sqrt[3]{{\sqrt 5 - 2}} + \sqrt[3]{{\sqrt 5 + 2}}} \right)\\
\to {E^3} = 2\sqrt 5 + 3E\\
\to {E^3} - 2\sqrt 5 - 3E = 0\\
\to {E^3} - \sqrt 5 {E^2} + \sqrt 5 {E^2} - 5E + 2E - 2\sqrt 5 = 0\\
\to {E^2}\left( {E - \sqrt 5 } \right) + \sqrt 5 E\left( {E - \sqrt 5 } \right) + 2\left( {E - \sqrt 5 } \right) = 0\\
\to \left[ \begin{array}{l}
E = \sqrt 5 \\
{E^2} + \sqrt 5 E + 2 = 0\left( {voli} \right)
\end{array} \right.\\
f.{F^3} = 364 + 3\sqrt[3]{{\left( {182 + \sqrt {33125} } \right)\left( {182 - \sqrt {33125} } \right)}}.\left( {\sqrt[3]{{182 + \sqrt {33125} }} + \sqrt[3]{{182 - \sqrt {33125} }}} \right)\\
\to {F^3} = 364 - 3F\\
\to \left( {F - 7} \right)\left( {{F^2} + 7F + 52} \right) = 0\\
\to \left[ \begin{array}{l}
F = 7\\
{F^2} + 7F + 52 = 0\left( {voli} \right)
\end{array} \right.
\end{array}\)
