20 БАЛЛОВ [latex] \frac{1}{ \sqrt{5}+ \sqrt{2} } + \frac{1}{ \sqrt{5}- \sqrt{2} } [/latex] [latex] \frac{ \sqrt{2} }{2- \sqrt{2} }+ \frac{ \sqrt{2} }{2+ \sqrt{2} } [/latex] [latex] \frac{2}{ \sqrt{2}+1 } - \frac{2}{ \sqrt{2}-1 ...
20 БАЛЛОВ
[latex] \frac{1}{ \sqrt{5}+ \sqrt{2} } + \frac{1}{ \sqrt{5}- \sqrt{2} } [/latex]
[latex] \frac{ \sqrt{2} }{2- \sqrt{2} }+ \frac{ \sqrt{2} }{2+ \sqrt{2} } [/latex]
[latex] \frac{2}{ \sqrt{2}+1 } - \frac{2}{ \sqrt{2}-1 } + \frac{3}{2 \sqrt{2} } [/latex]
[latex] \frac{3}{ \sqrt{3}+1 } - \frac{2}{1- \sqrt{3} } + \frac{3}{3 \sqrt{3} } [/latex]
Гость
Ответ(ы) на вопрос:
Гость1) [latex]\frac{1}{\sqrt{5} + \sqrt{2}} + \frac{1}{\sqrt{5} - \sqrt{2}} = \frac{\sqrt{5} - \sqrt{2}+ \sqrt{5} + \sqrt{2}}{(\sqrt{5} + \sqrt{2})(\sqrt{5}-\sqrt{2})} = \frac{2\sqrt{5}}{5-2} = \frac{2\sqrt{5}}{3}[/latex]
2) [latex]\frac{\sqrt{2}}{2-\sqrt{2}} + \frac{\sqrt{2}}{2+\sqrt{2}} = \frac{\sqrt{2}(2+\sqrt{2}) + \sqrt{2}(2-\sqrt{2})}{(2-\sqrt{2})(2+\sqrt{2})}=\frac{4\sqrt{2}}{4-2}=2\sqrt{2}[/latex]
3) [latex]\frac{2}{\sqrt{2}+1}-\frac{2}{\sqrt{2}-1} + \frac{3}{2\sqrt{2}}=\frac{2(\sqrt{2}-1) - 2(\sqrt{2}+1)}{(\sqrt{2}+1)(\sqrt{2}-1)} + \frac{3}{2\sqrt{2}}=\frac{-4}{1} + \frac{3}{2\sqrt{2}}=\frac{3-8\sqrt{2}}{2\sqrt{2}}[/latex]
4) [latex]\frac{3}{\sqrt{3}+1}-\frac{2}{1-\sqrt{3}} + \frac{3}{3\sqrt{3}}=\frac{3}{\sqrt{3}+1}+\frac{2}{\sqrt{3}-1} + \frac{1}{\sqrt{3}}=[/latex]
[latex]=\frac{3(\sqrt{3}-1)+2(\sqrt{3}+1)}{(\sqrt{3}+1)(\sqrt{3}-1)} + \frac{1}{\sqrt{3}}=\frac{5\sqrt{3}-1}{2}+\frac{1}{\sqrt{3}} = \frac{15-\sqrt{3}}{2\sqrt{3}}[/latex]
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