A More Difficult Number-Plus-Reciprocal Problem

Algebra Level 2

\[ x^{2048}+\frac{1}{x^{2048}}+x^{2047}-\frac{1}{x^{2047}}+\frac{1}{x^{2049}}-x^{2049}+2 \]

Find the value of the above expression if we know that \(x + \frac 1 x = 2\).

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