Đáp án: $1$
Giải thích các bước giải:
Ta có:
$\begin{split}2+\sqrt{5}&=\dfrac{8\left(2+\sqrt{5}\right)}{8}\\&=\dfrac{16+8\sqrt{5}}{8}\\&=\dfrac{1^3+3\cdot \:1^2\sqrt{5}+3\cdot \:1\cdot \left(\sqrt{5}\right)^2+\left(\sqrt{5}\right)^3}{8}\\&=\left(\dfrac{1+\sqrt{5}}{2}\right)^3\end{split}$
$\to \sqrt[3]{2+\sqrt{5}}=\dfrac{1+\sqrt{5}}{2}$
Tương tự $\sqrt[3]{2-\sqrt{5}}=\dfrac{1-\sqrt{5}}{2}$
$\to \sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}=\dfrac{1+\sqrt{5}}{2}+\dfrac{1-\sqrt{5}}{2}=1$
