[tex] \lim_{n \to \infty} \frac{2n^2+5n+2-an^2-bn-c}{\sqrt{2n^2+5n+2}+\sqrt{an^2+bn+c}} =5\sqrt{2}\\
\lim_{n \to \infty} \frac{(2-a)n^2+(5-b)n+2-c}{n(\sqrt{2+5/n+2/n^2}+\sqrt{a+b/n+c/n^2}} =5\sqrt{2}\\
2-a=0=\ \textgreater \ a=2\\
\frac{5-b}{\sqrt{2}+\sqrt{a} }=5\sqrt{2}=\ \textgreater \ b=-15\\
c\in R[/tex]
