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