Question

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

Answer 1

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

\(A=\frac{\sqrt{2}\left(\sqrt{3}-3\right)}{3+\sqrt{3}}+\frac{\sqrt{2}\left(\sqrt{3}+3\right)}{\sqrt{3}-3}=\frac{\sqrt{2}\left(\sqrt{3}-3\right)^2+\sqrt{2}\left(\sqrt{3}+3\right)^2}{3-9}=\frac{24\sqrt{2}}{-6}=-4\sqrt{2}\)