AoPS Academy
. I couldn't solve this and was wondering if any of you can find the pattern
If a problem has not been solved within 
days, then others are eligible to post a new probkem. Not only simple one-variable equations, but also systems of equations are allowed. The difficulty of these equations should be no less than that of typical quadratic one-variable equations. If the problem involves higher degrees or more variables, please ensure that the problem is solvable (i.e., has a definite solution, rather than an approximate one). Please indicate the domain of the solution to the equation (e.g., solve in 
, solve in 
).
that satises 
and 
for real 
and 
can be written as 
where the greatest common divisor of positive integers 
, 
, and 
is 
, and 
is not divisible by the square of any prime. Compute the value of 
.
does the following system of equations has a solution other than 
in the set of real numbers? 
where 
are positive integers satisfying the equations 
, , and be complex numbers such that they satisfy these equations:
If the maximum of 
can be expressed as 
for positive integers 
, 
, and 
, find the minimum possible value of 
.
![\[\begin{cases}
3x^2-2xy+3y^2+\dfrac{2}{x^2-2xy+y^2}=8\\
2x+\dfrac{1}{x-y}=4
\end{cases}\]](http://latex.artofproblemsolving.com/e/b/f/ebf41764f74c98da66dc31c48975f27bd734c334.png)
