Question

[Nguyễn Thế Anh]

\(\sqrt{ 6-\sqrt{11} } -\sqrt{ 6+\sqrt{11} }\)

Answer 1

[Dương Nhã Tịnh]

Đặt \(A=\sqrt{6-\sqrt{11}}-\sqrt{6+\sqrt{11}}\)

\(\Rightarrow A^2=6-\sqrt{11}-2\sqrt{\left(6-\sqrt{11}\right)\left(6+\sqrt{11}\right)}+6+\sqrt{11}\)

\(\Leftrightarrow A^2=12-2\sqrt{36-11}\)

\(\Leftrightarrow A^2=12-2.\sqrt{25}\)

\(\Leftrightarrow A^2=2\)(1)

Vì \(\hept{\begin{cases}\sqrt{6-\sqrt{11}}>0\\\sqrt{6+\sqrt{11}}>0\end{cases}}\)và \(6-\sqrt{11}< 6+\sqrt{11}\)

\(\Rightarrow A=\sqrt{6-\sqrt{11}}-\sqrt{6+\sqrt{11}}< 0\)(2)

Từ(1),(2) \(\Rightarrow A=-\sqrt{2}\)