is written in decimal form with n being a natural number, that it's decimal either terminates or is eventually periodic.
.
![\[\begin{cases}
3x^2-2xy+3y^2+\dfrac{2}{x^2-2xy+y^2}=8\\
2x+\dfrac{1}{x-y}=4
\end{cases}\]](http://latex.artofproblemsolving.com/e/b/f/ebf41764f74c98da66dc31c48975f27bd734c334.png)
and 
Prove that
Let 
Prove that
Let 
and 
Prove that
Let 
Prove that
be the roots of 
with 
and 
.![$[|3 \alpha |] + [|6 \beta|] +
[|9 \gamma |]$](http://latex.artofproblemsolving.com/9/f/f/9ffb5118d94f0e2fb84a411b47ec91c122985673.png)
is equal to
such that 
where degrees are used.
and 
Prove that
Let 
Prove that
be real numbers such that 
Prove that
Let 
Prove that
Let 
Prove that
Y by
As outlined in this (locked) post, the forum/blog creation message is out of date. It has been over a year since that post, and it still has not changed. I don't know if this got lost somewhere in the "passing this along" chain or if it was determined to be irrelevant, but it seems like a relatively simple fix 
