Question

Tính

\(\frac{6+4\sqrt{2}}{\sqrt{2}+\sqrt{6+4\sqrt{2}}}+\frac{6-4\sqrt{2}}{\sqrt{2}-\sqrt{6-4\sqrt{2}}}\)

Answer 1

\(=\frac{\left(2+\sqrt{2}\right)^2}{\sqrt{2}+\sqrt{\left(2+\sqrt{2}\right)^2}}+\frac{\left(2-\sqrt{2}\right)^2}{\sqrt{2}-\sqrt{\left(2-\sqrt{2}\right)^2}}\)

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