Giải thích các bước giải:
$\begin{array}{l} \left\{ \begin{array}{l} x + 2y = m + 3\\ 2x - 3y = m \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} 2(x + 2y) - (2x - 3y) = 2(m + 3) - m = m + 6\\ 2x - 3y = m \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} 7y = m + 6\\ 2x - 3y = m \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} y = \frac{{m + 6}}{7}\\ 2x = m + 3.\frac{{m + 6}}{7} \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} y = \frac{{m + 6}}{7}\\ x = \frac{{5m + 9}}{7} \end{array} \right. \end{array}$
$\begin{array}{l} \left\{ \begin{array}{l} y = \frac{{m + 6}}{7}\\ x = \frac{{5m + 9}}{7} \end{array} \right.\\ P = 98\left( {{x^2} + {y^2}} \right) + 4m\\ = 98({\frac{{5m + 9}}{7}^2} + {\frac{{m + 6}}{7}^2}) + 4m\\ = 52{m^2} + 1432m + 234\\ = 52({m^2} + \frac{{358}}{{13}} + \frac{9}{2})\\ = 52{(m + \frac{{179}}{{13}})^2} - \frac{{125122}}{{13}} \end{array}$
Vì $52{(m + \frac{{179}}{{13}})^2} \ge \forall x$
=> $P \ge - \frac{{125122}}{{13}}\forall x$
Dấu = xảy ra khi và chỉ khi m=$ - \frac{{179}}{{13}}$
