Question

 

giúp mình câu 11 và câu 12 với ạ

 

Answer 1

11: \(=\dfrac{\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{5}-1+\sqrt{5}+1}{\sqrt{2}}\)

\(=\dfrac{2\sqrt{5}}{\sqrt{2}}=\sqrt{10}\)

12: \(A^2=4+\sqrt{10+2\sqrt{5}}+4-\sqrt{10+2\sqrt{5}}+2\cdot\sqrt{16-\left(10+2\sqrt{5}\right)}\)

\(=8+2\cdot\sqrt{6-2\sqrt{5}}\)

\(=8+2\left(\sqrt{5}-1\right)=6+2\sqrt{5}\)

\(\Leftrightarrow A=\sqrt{5}+1\)