$\begin{array}{l}
P:\,\,\forall x;\,\,y \in R:\,\,\,{x^2} + 5{y^2} - 4xy + 2x - 6y + 3 > 0\\
{x^2} + 5{y^2} - 4xy + 2x - 6y + 3\\
= {x^2} + 2x + 4{y^2} - 4xy + 1 - 4y + {y^2} - 2y + 1 + 1\\
= {\left( {x - 2y + 1} \right)^2} + {\left( {y - 1} \right)^2} + 1 \ge 1\,\,\,\forall x,\,\,y\\
\Rightarrow P\,\,dung.
\end{array}$