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2/\sqrt{4-3\sqrt[4]{5}+2\sqrt[4]{25}-\sqrt[4]{125}} 2018 Ecuador NMO (OMEC) 3.6

Source:

September 18, 2021
algebraRadicals

Problem Statement

Reduce 24−354+2254−1254\frac{2}{\sqrt{4-3\sqrt[4]{5} + 2\sqrt[4]{25}-\sqrt[4]{125}}} to its lowest form.
Then generalize this result and show that it holds for any positive nn.
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