Given, x = 7 + 4√3 , xy = 1
Y = \(\frac{1}{x}\) = \(\frac{1}{7}\)+ 4√3 = 7 - 4√3
Y2 = \(\frac{1}{x^2}\) = 49 + 48 - 56√3 = 97 - 56√3
Similarly, x = \(\frac{1}{y}\)
= x2 = \(\frac{1}{y^2}\) = ( 7 + 4√3)2 = 49 + 48 + 56√3 = 97+ 56√3
So, \(\frac{1}{x^2}\) + \(\frac{1}{y^2}\) = 97 + 56√3 + 97 – 56√3 = 194