Answer :

Given . x = 7+4√3 , xy = 1


Y = 1/x = 1/7+ 4√3 = 7-4√3


Y2 = 1/x2 = 49 + 48 - 56√3 = 97 - 56√3


Similarly, x = 1/y


= x2 = 1/y2 = ( 7 +4√3)2 = 49 + 48 + 56√3 = 97+ 56√3


So, 1/x2 + 1/y2 = 97 + 56√3 + 97 – 56√3 = 194

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