Expansions-7

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If a 2 - 5 a + 1 = 0 and a is not equal to 0, find :

(i) a + 1 / a (ii) a 2 + 1 / a 2

Solution :

(i) a 2 - 5 a + 1 = 0

=> a 2 / a - 5 a / a + 1 / a = 0 [Dividing each term by a]

=> a - 5 + 1 / a = 0

=> a + 1 / a = 5

(ii) a 2 + 1 / a 2 = (a + 1 / a) 2 - 2 = 5 2 - 2 = 25 - 2 = 23

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