Помогите пожалуйста!

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Помогите пожалуйста! ( \sqrt{ \sqrt{3}+ \sqrt{2} } - \sqrt{ \sqrt{3}- \sqrt{2} } )*( \sqrt{ \sqrt{3}+ \sqrt{2} }+ \sqrt{ \sqrt{3}- \sqrt{2} } ) ^{-1} + \sqrt{ \sqrt{( \sqrt{5}- \frac{5}{2}) ^{2} }- \sqrt[3]{( \frac{3}{2}- \sqrt{5) } ^{3} } } }


Алгебра (403 баллов) | 33 просмотров
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Решите задачу:

(\sqrt{\sqrt{3}+\sqrt{2}}-\sqrt{\sqrt{3}-\sqrt{2}})*(\sqrt{\sqrt{3}+\sqrt{2}}+\sqrt{\sqrt{3}-\sqrt{2}}) ^{-1} +\sqrt{\sqrt{(\sqrt{5}-\frac{5}{2})^{2}}-\sqrt[3]{(\frac{3}{2}-\sqrt{5)}^{3}}}}=\\\ 
=\frac{\sqrt{\sqrt{3}+\sqrt{2}}-\sqrt{\sqrt{3}-\sqrt{2}}}{\sqrt{\sqrt{3}+\sqrt{2}}+\sqrt{\sqrt{3}-\sqrt{2}}} +\sqrt{|\sqrt{5}-\frac{5}{2}|-\frac{3}{2}+\sqrt{5)}}=\\\
=\frac{\sqrt{\sqrt{3}+\sqrt{2}}-\sqrt{\sqrt{3}-\sqrt{2}}}{\sqrt{\sqrt{3}+\sqrt{2}}+\sqrt{\sqrt{3}-\sqrt{2}}} +\sqrt{\frac{5}{2}-\sqrt{5}-\frac{3}{2}+\sqrt{5}}=\\\
=\frac{\sqrt{\sqrt{3}+\sqrt{2}}-\sqrt{\sqrt{3}-\sqrt{2}}}{\sqrt{\sqrt{3}+\sqrt{2}}+\sqrt{\sqrt{3}-\sqrt{2}}} +1=\frac{(\sqrt{\sqrt{3}+\sqrt{2}}-\sqrt{\sqrt{3}-\sqrt{2}})^2}{(\sqrt{\sqrt{3}+\sqrt{2}}+\sqrt{\sqrt{3}-\sqrt{2}})(\sqrt{\sqrt{3}+\sqrt{2}}-\sqrt{\sqrt{3}-\sqrt{2}})} +1=\\\
=\frac{(\sqrt{\sqrt{3}+\sqrt{2}})^2-2\sqrt{\sqrt{3}+\sqrt{2}}*\sqrt{\sqrt{3}-\sqrt{2}}+(\sqrt{\sqrt{3}-\sqrt{2}}))^2}{(\sqrt{\sqrt{3}+\sqrt{2}})^2-(\sqrt{\sqrt{3}-\sqrt{2}})^2} +1=
=\frac{\sqrt{3}+\sqrt{2}-2+\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}}+1\\\
=\frac{2\sqrt{3}-2}{2\sqrt{2}}+1=\frac{2\sqrt{3}-2+2\sqrt{2}}{2\sqrt{2}}=\frac{\sqrt{3}-1+\sqrt{2}}{\sqrt{2}}
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