Đáp án:
$\begin{array}{l}
1)A = 9{x^2} - 12x\\
= {\left( {3x} \right)^2} - 2.3x.2 + 4 - 4\\
= {\left( {3x - 2} \right)^2} - 4 \ge - 4\\
\Leftrightarrow GTNN:A = - 4\,khi:x = \dfrac{2}{3}\\
2)\\
B = 2x - {x^2} - 2\\
= - \left( {{x^2} - 2x + 1} \right) - 1\\
= - {\left( {x - 1} \right)^2} - 1 \le - 1\\
\Leftrightarrow GTLN:B = - 1\,khi:x = 1\\
3){\left( {5x - 1} \right)^2} - \left( {5x - 4} \right)\left( {5x + 4} \right) + 7 = 0\\
\Leftrightarrow 25{x^2} - 10x + 1 - \left( {25{x^2} - 16} \right) + 7 = 0\\
\Leftrightarrow 25{x^2} - 10x + 1 - 25{x^2} + 16 + 7 = 0\\
\Leftrightarrow 20x = 24\\
\Leftrightarrow x = \dfrac{6}{5}\\
Vay\,x = \dfrac{6}{5}\\
4)\\
a){\left( {3x - 2} \right)^2} + {\left( {3x + 2} \right)^2} + 2.\left( {9{x^2} - 4} \right)\\
= {\left( {3x - 2} \right)^2} + 2.\left( {3x - 2} \right)\left( {3x + 2} \right) + {\left( {3x + 2} \right)^2}\\
= {\left( {3x - 2 + 3x + 2} \right)^2}\\
= {\left( {6x} \right)^2}\\
= 36{x^2}\\
= 36.{\left( {\dfrac{{ - 1}}{3}} \right)^2}\\
= 4\\
b)4{x^2} - 20x + 27\\
= {\left( {2x} \right)^2} - 2.2x.5 + 25 + 2\\
= {\left( {2x - 5} \right)^2} + 2\\
= {\left( {2.52,5 - 5} \right)^2} + 2\\
= {\left( {105 - 5} \right)^2} + 2\\
= {100^2} + 2\\
= 10002
\end{array}$
