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2

Part of 2001 Swedish Mathematical Competition

Problems(1)

\sqrt[3]{(\sqrt{52} + 5}- \sqrt[3]{\sqrt{52}- 5} is rational

Source: 2001 Swedish Mathematical Competition p2

3/21/2021
Show that 52+53−52−53\sqrt[3]{\sqrt{52} + 5}- \sqrt[3]{\sqrt{52}- 5} is rational.
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