Đáp án:
$\begin{array}{l}
T = {\left( {3x - 2} \right)^2} - {\left( {3 + 2x} \right)^2}\\
= 9{x^2} - 12x + 4 - \left( {4{x^2} + 12x + 9} \right)\\
= 5{x^2} - 24x - 5\\
= 5.\left( {{x^2} - 2.x.\dfrac{{12}}{5} + \dfrac{{144}}{{25}}} \right) - 5.\dfrac{{144}}{{25}} - 5\\
= 5.{\left( {x - \dfrac{{12}}{5}} \right)^2} - \dfrac{{169}}{5} \ge \dfrac{{ - 169}}{5}\\
\Rightarrow T \ge \dfrac{{ - 169}}{5}\\
\Rightarrow GTNN:T = \dfrac{{ - 169}}{5}\\
Khi:x = \dfrac{{12}}{5}\\
X = {\left( {5x - 6} \right)^2} - 2{\left( {3x + 4} \right)^2}\\
= 25{x^2} - 60x + 36 - 2.\left( {9{x^2} + 24x + 16} \right)\\
= 7{x^2} - 108x + 4\\
= 7.\left( {{x^2} - 2.x.\dfrac{{54}}{7} + \dfrac{{{{54}^2}}}{{{7^2}}}} \right) - 7.\dfrac{{{{54}^2}}}{{{7^2}}} + 4\\
= 7.{\left( {x - \dfrac{{54}}{7}} \right)^2} - \dfrac{{188}}{7} \ge \dfrac{{ - 188}}{7}\\
\Rightarrow GTNN:X = - \dfrac{{188}}{7}\\
Khi:x = \dfrac{{54}}{7}
\end{array}$
