Find all positive solution of system of equation: $ \frac{xy}{2005y+2004x}+\frac{yz}{2004z+2003y}+\frac{zx}{2003x+2005z}=\frac{x^{2}+y^{2}+z^{2}}{2005^{2}+2004^{2}+2003^{2}}$

Real numbers $ x_{1},x_{2},..,x_{n}$ are positive. Prove the inequality: $ \frac{x_{1}}{x_{2}+x_{3}}+\frac{x_{2}}{x_{3}+x_{4}}+...+ \frac{x_{n-1}}{x_{n}+x_{1}}+\frac{x_{n}}{x_{1}+x_{2}}>(\sqrt{2}-1)n$

Determine all strictly increasing functions $ f: R\rightarrow R$ satisfying relationship $ f(x+f(y))=f(x+y)+2005$ for any real values of x and y.

Let $a$ and $b$ be two real numbers. Find these numbers given that the graphs of $f:\mathbb{R} \to \mathbb{R} , f(x)=2x^4-a^2x^2+b-1$ and $g:\mathbb{R} \to \mathbb{R} ,g(x)=2ax^3-1$ have exactly two points of intersection.