NVAMediumJEE Main 2025 · 4 April, Shift 2Sum of Series

Mathematics Question from JEE Main 2025 · 4 April, Shift 2

If α\alpha is a root of the equation x2+x+1=0x^2 + x + 1 = 0 and k=1n(αk+1αk)2=20,\sum_{k=1}^{n} \left( \alpha^k + \frac{1}{\alpha^k} \right)^2 = 20, then nn is equal to _____

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