1. Commutative Rings and units

Let R = { $m+n*\sqrt{2}$ | $m,n \in Z$}

Q: Show that $1+2\sqrt{2}$ has infinite order in $R^x$

From previous part of the Problem:
$m+n*\sqrt{2}$ is a unit in R if and only if $m^2-2n^2= \pm{1}$

I'm a little confused by this since according to the above theorem $1+2\sqrt{2}$ is not a unit

What am I missing? Is it actually a unit?

2. disregard this thread. Its a typo in the book