Expansions-5

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If x + 1 / x = 2 , find : (i) x2 + 1 / x 2 (ii) x 4 + 1 / x 4

Solution :

(i) x 2 + 1 / x 2 = (x + 1 / x) 2 - 2 = (2) 2 - 2 = 4 - 2 = 2

(ii) x 4 + 1 / x 4 = (x 2 + 1 / x 2 ) - 2 = 2 2 - 2 = 4 - 2 = 2

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