Ответ:

[tex]\frac{10}{2\sqrt{3-\sqrt{2} } } = \frac{15\sqrt{3-\sqrt{2} }+5\sqrt{6-2\sqrt{2} } }{7}[/tex]

Пошаговое объяснение:

[tex]\frac{10 }{2\sqrt{3-\sqrt{2} }} =\frac{5}{\sqrt{3-\sqrt{2} } } =\\ \\ \frac{5}{\sqrt{3-\sqrt{2} } }\times\frac{\sqrt{3-\sqrt{2} } }{\sqrt{3-\sqrt{2} } } =\\ \\ \frac{5\times\sqrt{3-\sqrt{2} } }{\sqrt{3-\sqrt{2} } \times\sqrt{3-\sqrt{2} } } =\\ \\ \frac{5\sqrt{3-\sqrt{2} } }{3-\sqrt{2} } =\frac{5\sqrt{3-\sqrt{2} } }{3-\sqrt{2} }\times\frac{3+\sqrt{2} }{3+\sqrt{2} } =\\ \\ \frac{5\sqrt{3-\sqrt{2} } (3+\sqrt{2} )}{(3-\sqrt{2} )(3+\sqrt{2} )} =\frac{15\sqrt{3-\sqrt{2} }+ 5\sqrt{(3-\sqrt{2} )\times2} }{9-2}=[/tex]

[tex]\frac{15\sqrt{3-\sqrt{2} }+5\sqrt{6-2\sqrt{2} } }{7}[/tex]