Đáp án:
`49)` `-\sqrt{2}`
`50)` `-2\sqrt{2}`
Giải thích các bước giải:
`49)` `\sqrt{2/{7+3\sqrt{5}}}+2/{3-\sqrt{5}}-{2+3\sqrt{2}}/\sqrt{2}`
`=\sqrt{{2(7-3\sqrt{5})}/{(7+3\sqrt{5}).(7-3\sqrt{5})}}+{2(3+\sqrt{5})}/{(3-\sqrt{5}).(3+\sqrt{5})}-{\sqrt{2}.(\sqrt{2}+3)}/\sqrt{2}`
`=\sqrt{{14-6\sqrt{5}}/{7^2-(3\sqrt{5})^2}}+{2(3+\sqrt{5})}/{3^2-5}-(\sqrt{2}+3)`
`=\sqrt{{3^2-2.3.\sqrt{5}+5}/4}+{3+\sqrt{5}}/2-(\sqrt{2}+3)`
`=\sqrt{{(3-\sqrt{5})^2}/{2^2}}+{3+\sqrt{5}}/2-\sqrt{2}-3`
`={3-\sqrt{5}}/2+{3+\sqrt{5}}/2-\sqrt{2}-3`
`={3-\sqrt{5}+3+\sqrt{5}}/2-\sqrt{2}-3`
`=3-\sqrt{2}-3=-\sqrt{2}`
$\\$
`50)` `1/{\sqrt{2}-\sqrt{3}}+\sqrt{2}/{2+\sqrt{6}}`
`=1/{\sqrt{2}-\sqrt{3}}+\sqrt{2}/{\sqrt{2}(\sqrt{2}+\sqrt{3})}`
`=1/{\sqrt{2}-\sqrt{3}}+1/{\sqrt{2}+\sqrt{3}}`
`={\sqrt{2}+\sqrt{3}+\sqrt{2}-\sqrt{3}}/{(\sqrt{2}-\sqrt{3})(\sqrt{2}+\sqrt{3})}`
`={2\sqrt{2}}/{2-3}=-2\sqrt{2}`