If (a² - 4a - 1) = 0 and a ≠ 0, find the values of: (i) (a - 1/a) (ii) (a + 1/a) (iii) (a² - 1/a²) (iv) (a² + 1/a²)

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Using (a + b)² = (a² + b² + 2ab), evaluate:
(i) (137)²
(ii) (1008)²
(iii) (11.6)²