$2a=\sqrt{5}+1,2b=\sqrt{5}-1,c=\sqrt[4]{5}$
$\displaystyle\begin{pmatrix}x\\y\end{pmatrix}=
\begin{pmatrix}\frac{2}{\sqrt{10-2\sqrt{5}}} & \frac{1-\sqrt{5}}{\sqrt{10-2\sqrt{5}}}\\\frac{\sqrt{5}-1}{\sqrt{10-2\sqrt{5}}} & \frac{2}{\sqrt{10-2\sqrt{5}}}\end{pmatrix} \begin{pmatrix}\pm\sqrt[4]{5}\\0\end{pmatrix}=\begin{pmatrix}\frac{\pm2\sqrt[4]{5}}{\sqrt{10-2\sqrt{5}}}\\\frac{\pm\sqrt[4]{5}(\sqrt{5}-1)}{\sqrt{10-2\sqrt{5}}}\end{pmatrix}$
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