Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
{x^2} + 4{y^2} - 2x - 4xy + 4y + 2020\\
= \left( {{x^2} - 4xy + 4{y^2}} \right) - \left( {2x - 4y} \right) + 2020\\
= {\left( {x - 2y} \right)^2} - 2.\left( {x - 2y} \right) + 2020\\
= \left[ {{{\left( {x - 2y} \right)}^2} - 2.\left( {x - 2y} \right) + 1} \right] + 2019\\
= {\left[ {\left( {x - 2y} \right) - 1} \right]^2} + 2019\\
= {\left( {x - 2y - 1} \right)^2} + 2019\\
{\left( {x - 2y - 1} \right)^2} \ge 0,\,\,\,\forall x,y\\
\Rightarrow {\left( {x - 2y - 1} \right)^2} + 2019 \ge 2019 > 0,\,\,\,\forall x,y\\
\Rightarrow {x^2} + 4{y^2} - 2x - 4xy + 4y + 2020 > 0,\,\,\,\forall x,y
\end{array}\)
