Using the identity (x - 1/x) squared = x squared - 2 + 1/x squared, we get 9 = x squared + 1/x squared - 2, so x squared + 1/x squared = 11.
Note: The NTA key marks option 7, which is obtained only if the question is read as x + 1/x = 3; we have solved the question as written (x - 1/x = 3), giving 11.