Đáp án: $\,\sqrt[3]{{5 - 2\sqrt 6 }} + \sqrt[3]{{5 + 2\sqrt 6 }} = 2,61$
Giải thích các bước giải:
$\begin{array}{l}
x = \sqrt[3]{{5 - 2\sqrt 6 }} + \sqrt[3]{{5 + 2\sqrt 6 }}\\
\Leftrightarrow {x^3} = 5 - 2\sqrt 6 + 3.{\left( {\sqrt[3]{{5 - 2\sqrt 6 }}} \right)^2}.\sqrt[3]{{5 + 2\sqrt 6 }}\\
+ 3.\sqrt[3]{{5 - 2\sqrt 6 }}.{\left( {\sqrt[3]{{5 + 2\sqrt 6 }}} \right)^2} + 5 + 2\sqrt 6 \\
\Leftrightarrow {x^3} = 10\\
+ 3.\sqrt[3]{{5 - 2\sqrt 6 }}.\sqrt[3]{{5 + 2\sqrt 6 }}.\left( {\sqrt[3]{{5 - 2\sqrt 6 }} + \sqrt[3]{{5 + 2\sqrt 6 }}} \right)\\
\Leftrightarrow {x^3} = 10 + 3.\sqrt[3]{{{5^2} - {{\left( {2\sqrt 6 } \right)}^2}}}.x\\
\Leftrightarrow {x^3} - 3.x - 10 = 0\\
\Leftrightarrow x = 2,61\\
Vậy\,\sqrt[3]{{5 - 2\sqrt 6 }} + \sqrt[3]{{5 + 2\sqrt 6 }} = 2,61
\end{array}$
