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

Source: 2001 Swedish Mathematical Competition p2

March 21, 2021
algebrarationalradical

Problem Statement

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