$$t = \sqrt { 2 } + 1 , t + \frac { 1 } { t }$$
$u=2\sqrt{2}\approx 2.828427125$
$$u=\sqrt{2}+1+\frac{1}{\sqrt{2}+1}$$
$$u=\sqrt{2}+1+\frac{\sqrt{2}-1}{\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)}$$
$$u=\sqrt{2}+1+\frac{\sqrt{2}-1}{\left(\sqrt{2}\right)^{2}-1^{2}}$$
$$u=\sqrt{2}+1+\frac{\sqrt{2}-1}{2-1}$$
$$u=\sqrt{2}+1+\frac{\sqrt{2}-1}{1}$$
$$u=\sqrt{2}+1+\sqrt{2}-1$$
$$u=2\sqrt{2}+1-1$$
$$u=2\sqrt{2}$$
$$t=\sqrt{2}+1$$ $$u=2\sqrt{2}$$
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