Experts, Meritnation

I am unable to solve one of the questions of my Olympiad book. This was the question:

$If \text{'}\text{'}x = \sqrt{3} - 1\text{'}\text{'}, then find the value of {\left\{x+\frac{1}{x}\right\}}^2$


Please help me to solve this. When I saw the answer key in the Olympiad book, the answer shown was  $7-\frac{3\left(\sqrt{3}\right)}{2}$, but solution was not given in the book.