$$x = 4 - \sqrt { 15 } , x + \frac { 1 } { x }$$
$y=8$
$$y=4-\sqrt{15}+\frac{1}{4-\sqrt{15}}$$
$$y=4-\sqrt{15}+\frac{4+\sqrt{15}}{\left(4-\sqrt{15}\right)\left(4+\sqrt{15}\right)}$$
$$y=4-\sqrt{15}+\frac{4+\sqrt{15}}{4^{2}-\left(\sqrt{15}\right)^{2}}$$
$$y=4-\sqrt{15}+\frac{4+\sqrt{15}}{16-15}$$
$$y=4-\sqrt{15}+\frac{4+\sqrt{15}}{1}$$
$$y=4-\sqrt{15}+4+\sqrt{15}$$
$$y=8-\sqrt{15}+\sqrt{15}$$
$$y=8$$
$$x=4-\sqrt{15}$$ $$y=8$$
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