Let $ABC$ be a triangle such that $\angle ACB=\large\frac{\pi}{6}$.Let $a,b$ and $c$ denote the lengths of the sides opposite to $A,B$ and $C$ respectively.The value of $x$ for which $a=x^2+x+1,b=x^2-1$ and $c=2x+1$ is

Question

$\begin{array}{1 1}(a)\;-(2+\sqrt 3)&(b)\;1+\sqrt 3\\(c)\;2+\sqrt 3&(d)\;4\sqrt 3\end{array}$