If a^2 - 5a - 1 = 0 and a ≠ 0, find : (i) a - 1/a (ii) a + 1/a (iii) a^2 - 1/a^2

(i) Given, ⇒ a 2 - 5a - 1 = 0 ⇒ a 2 - 1 = 5a Dividing above equation by a, we get : Hence, . (ii) By formula, Hence, . (iii) By formula, Hence, .