Question

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

Answer 1

Đề yêu cầu gì á em?

Answer 2

căn bậc hai(5)+3*căn bậc hai(2)

Answer 3

\(A=\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}\\ \Leftrightarrow A^3=2+\sqrt{5}+2-\sqrt{5}+3\sqrt[3]{\left(2+\sqrt{5}\right)\left(2-\sqrt{5}\right)}\left(\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}\right)\\ \Leftrightarrow A^3=4+3A\sqrt[3]{-1}\\ \Leftrightarrow A^3+3A-4=0\\ \Leftrightarrow A^3-A^2+A^2-A+4A-4=0\\ \Leftrightarrow\left(A-1\right)\left(A^2+A+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}A=1\\A^2+A+4=0\left(1\right)\end{matrix}\right.\\ \Delta\left(1\right)=1-4=-3< 0\Leftrightarrow A=1\)