$$x = \sqrt { 3 } + 1 , ( x + \frac { 2 } { x } ) ^ { 2 }$$
$y=12$
$$y=\left(\sqrt{3}+1+\frac{2}{\sqrt{3}+1}\right)^{2}$$
$$y=\left(\sqrt{3}+1+\frac{2\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}\right)^{2}$$
$$y=\left(\sqrt{3}+1+\frac{2\left(\sqrt{3}-1\right)}{\left(\sqrt{3}\right)^{2}-1^{2}}\right)^{2}$$
$$y=\left(\sqrt{3}+1+\frac{2\left(\sqrt{3}-1\right)}{3-1}\right)^{2}$$
$$y=\left(\sqrt{3}+1+\frac{2\left(\sqrt{3}-1\right)}{2}\right)^{2}$$
$$y=\left(\sqrt{3}+1+\sqrt{3}-1\right)^{2}$$
$$y=\left(2\sqrt{3}+1-1\right)^{2}$$
$$y=\left(2\sqrt{3}\right)^{2}$$
$$y=2^{2}\left(\sqrt{3}\right)^{2}$$
$$y=4\left(\sqrt{3}\right)^{2}$$
$$y=4\times 3$$
$$y=12$$
$$x=\sqrt{3}+1$$ $$y=12$$
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