Question

[Lê Minh Đức]

Help me! Cần gấp

Answer 1

[Arima Kousei]

\(A=\frac{\sqrt{x}+1}{\sqrt{x}-2}\)

\(x=\sqrt{6-4\sqrt{2}}+\sqrt{6+4\sqrt{2}}-2\sqrt{3}\) \(=\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{\left(2+\sqrt{2}\right)^2}-2\sqrt{3}\)

\(=2-\sqrt{2}+2+\sqrt{2}-2\sqrt{3}=4-2\sqrt{3}=\left(\sqrt{3}-1\right)^2\)

\(\sqrt{x}=\sqrt{3}-1\)

\(A=\frac{\sqrt{3}-1+1}{\sqrt{3}-1-2}=\frac{\sqrt{3}}{\sqrt{3}-3}=\frac{1}{1-\sqrt{3}}\)