If \(\mathbf{x}+\left(\frac{1}{x}\right)=\frac{(\sqrt{3}+1)}{2}\) then what is the value of x4 + \( \left(\frac{1}{x^4}\right)\)?
1
\(\frac{(4 \sqrt{3}-1)}{4}\)
2
\(\frac{(4 \sqrt{3}+1)}{4}\)
3
\(\frac{(-4 \sqrt{3}-1)}{4}\)
4
\(\frac{(-4 \sqrt{3}+1)}{4}\)