Question 828975
{{{(x+ 1/x)^2=3}}}
take square root of each side
{{{(x+ 1/x)=sqrt(3)}}}
multiply each side by x
{{{(x^2+ 1)=sqrt(3)x}}}
subtract sqrt(3)x from each side
{{{x^2-sqrt(3)x+1=0}}}
Solutions are
{{{x=(1/2)(sqrt(3)-i)}}} or {{{x=(1/2)(sqrt(3)+i)}}}
See http://www.wolframalpha.com/input/?i=x^2-sqrt%283%29x%2B1%3D0

below is the solution by the solver
*[invoke quadratic "x", 1, -sqrt(3), 1 ]

Plugging solutions back into the equation will take some careful work.