Expansions-6

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Given : a 2 + 1 / a 2 = 7, find :

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

Solution :

(i) ( a + 1 / a ) 2 = a 2 + 1 / a 2 + 2 = 7 + 2 = 9

=> a + 1 / a = ± √9 = ± 3

(ii) Since, ( a - 1 / a ) 2 = a 2 + 1 / a 2 - 2 = 7 - 2 = 5

=> a - 1 / a = ± √5

(iii) a 2 - 1 / a 2 = ( a + 1 / a ) (a - 1 / a) = ± 3 √5

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