\(T=\frac{\sqrt{2}.\left(4+\sqrt{7}\right)}{\sqrt{2}.\left(2\sqrt{2}+\sqrt{4+\sqrt{7}}\right)}+\frac{\sqrt{2}.\left(4-\sqrt{7}\right)}{\sqrt{2}.\left(2\sqrt{2}-\sqrt{4-\sqrt{7}}\right)}\)
\(T=\frac{4\sqrt{2}+\sqrt{14}}{4+\sqrt{8+2\sqrt{7}}}+\frac{4\sqrt{2}-\sqrt{14}}{4-\sqrt{8-2\sqrt{7}}}\)
\(T=\frac{4\sqrt{2}+\sqrt{14}}{4+\sqrt{7+2\sqrt{7}+1}}+\frac{4\sqrt{2}-\sqrt{14}}{4-\sqrt{7-2\sqrt{7}+1}}\)
\(T=\frac{4\sqrt{2}+\sqrt{14}}{4+\left(\sqrt{7}+1\right)^2}+\frac{4\sqrt{2}-\sqrt{14}}{4-\left(\sqrt{7}-1\right)^2}\)\(T=\frac{4\sqrt{2}+\sqrt{14}}{4+|\sqrt{7}+1|}+\frac{4\sqrt{2}-\sqrt{14}}{4-|\sqrt{7}-1|}\)
\(T=\frac{4\sqrt{2}+\sqrt{14}}{4+\sqrt{7}+1}+\frac{4\sqrt{2}-\sqrt{14}}{4-\sqrt{7}+1}\)
\(T=\frac{4\sqrt{2}+\sqrt{14}}{5+\sqrt{7}}+\frac{4\sqrt{2}-\sqrt{14}}{5-\sqrt{7}}\)
\(T=\frac{\left(4\sqrt{2}+\sqrt{14}\right).\left(5-\sqrt{7}\right)}{\left(5+\sqrt{7}\right).\left(5-\sqrt{7}\right)}+\frac{\left(4\sqrt{2}-\sqrt{14}\right).\left(5+\sqrt{7}\right)}{\left(5+\sqrt{7}\right).\left(5-\sqrt{7}\right)}\)
\(T=\frac{20\sqrt{2}-\sqrt{98}}{9}\)
\(T=\frac{13\sqrt{2}}{9}\)
