Question

If x – 1/x = 3 + 2 root2, find the value of x^2 + 1/x^2​

Answer 1

x = 3-2√2

x2 = (3-2√2)2 = 9+8-12√2 = 17-12√2

1/x2= 1/17-12√2

Rationalise The Denominator

1*17+12√2 / (17-12√2 ) * (17+12√2) = 17+12√2/289-288 = 17+12√2

Now Add We Get

17-12√2+17+12√2 = 34

So Answer - 34