![\[\begin{cases}
3x^2-2xy+3y^2+\dfrac{2}{x^2-2xy+y^2}=8\\
2x+\dfrac{1}{x-y}=4
\end{cases}\]](http://latex.artofproblemsolving.com/e/b/f/ebf41764f74c98da66dc31c48975f27bd734c334.png)
and 
be 2 distinct positive integers.
be in an integer. Prove why ?
other than a polynomial satisfying
Prove that
.
-
,
be the midpoint of side 
and 
be the midpoint of segment 
.
and 
intersect at 
.
.
such that 
is a square perfect.
friends in this. However, if two people are not friends at least they have a friend in this party. What is the largest possible number of people in the party?
of positive integers which satisfy the equation 
,
,
,
and circumcircle 
,
be the circle that is tangent to 
,
,
denote the incenters of 
,
,
,
.
.
on both sides and resubstituting 
,
.
,
,
We already have our base case. 
.
.
t
So,
and
Are these identities useful? And can you use them to compute the sum?
is on the curve 
.
with focus 
on 
,
and 
respectively. The line 
parallel to the line 
.
have two intersection points, find the range of 
.
.
, then 
, so 
,and 
.
.
The answer is that according to the question, the equation has two negative roots. I can't understand this, and this is exactly where my problem lies.\
.
.
Y by
When exporting a rich format document in the writing tab into the message board, bold formatting specifically is broken and results in broken BBCode.
Page URL: virtual.aopsacademy.org/class/<any writing class works here>/writing
TO REPRODUCE
1. enter "Lorem ipsum".
2. apply bold to "Lorem"
3. apply italic to "ip".
4. click the Post Draft on Message Board
5. read the contents of the message board post.
FOR EXAMPLE
When I format "Lorem ipsum" (in the writing tab of course), but when I export to post it, I get
Notice that the first bolding does not start, only ends.
Page URL: virtual.aopsacademy.org/class/<any writing class works here>/writing
TO REPRODUCE
1. enter "Lorem ipsum".
2. apply bold to "Lorem"
3. apply italic to "ip".
4. click the Post Draft on Message Board
5. read the contents of the message board post.
FOR EXAMPLE
When I format "Lorem ipsum" (in the writing tab of course), but when I export to post it, I get
Lorem[/b] [i]ip[/i]sumNotice that the first bolding does not start, only ends.
