Algebra · Nested radicals · Irrationality · Absolute value · Estimation
Determine all positive integers \(n\) for which the number
\[ \left| n - \sqrt{6 + \sqrt{6 + \sqrt{6}}} \right| + \left| 3 - \sqrt{6 + \sqrt{6 + \sqrt{6}}} \right| \]
is rational.
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Serbian Regional Competition 2011, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source