Observe that
[tex] \left(x-\frac{1}{x}\right)^2 = x^2 + \frac{1}{x^2} - 2 [/tex]
but since [tex] \x-\frac{1}{x} = \sqrt{3} [/tex], we can rewrite it as
[tex] (\sqrt{3})^2 = x^2+\frac{1}{x^2}-2 \iff x^2+\frac{1}{x^2} = 3+2 = 5 [/tex]
So, the answer is [tex] 5 [/tex]
