請教一題

請教一題,如附件,謝謝!!

\(\alpha\) 為 \(x^2-3x+1=0\) 之一根， \(\beta\) 為 \(x^2-2x-1=0\) 之一根，求

\(\displaystyle\left\{\begin{matrix}\displaystyle\left(\beta^2+\frac{1}{\beta^2}\right)X+\left(\alpha^2+\frac{1}{\alpha^2}\right)Y=\alpha^4+\frac{1}{\alpha^4}  \\ \left(\alpha^3+\frac{1}{\alpha^3}\right)X-\left(\beta^3-\frac{1}{\beta^3}\right)Y=-\left(\beta^4+\frac{1}{\beta^4}\right)\\  \end{matrix} \right.\) 之 \(X\) 解?