Đáp án:
$\begin{array}{l}
B1)\\
A = 5x - {x^2} = \\
= - \left( {{x^2} - 5x} \right)\\
= - \left( {{x^2} - 2.x.\dfrac{5}{2} + \dfrac{{25}}{4}} \right) + \dfrac{{25}}{4}\\
= - {\left( {x - \dfrac{5}{2}} \right)^2} + \dfrac{{25}}{4} \le \dfrac{{25}}{4}\,\\
\Leftrightarrow GTLN:A = \dfrac{{25}}{4}\,khi:x = \dfrac{5}{2}\\
B = x - {x^2}\\
= - \left( {{x^2} - x} \right)\\
= - \left( {{x^2} - 2.x.\dfrac{1}{2} + \dfrac{1}{4}} \right) + \dfrac{1}{4}\\
= - {\left( {x - \dfrac{1}{2}} \right)^2} + \dfrac{1}{4} \le \dfrac{1}{4}\\
\Leftrightarrow GTLN:B = \dfrac{1}{4}\,khi:x = \dfrac{1}{2}\\
C = 4x - {x^2} + 3\\
= - \left( {{x^2} - 4x + 4} \right) + 4 + 3\\
= - {\left( {x - 2} \right)^2} + 7 \le 7\\
\Leftrightarrow GTLN:C = 7\,khi:x = 2\\
D = - {x^2} + 6x - 11\\
= - \left( {{x^2} - 6x + 9} \right) + 9 - 11\\
= - {\left( {x - 3} \right)^2} - 2 \le - 2\\
\Leftrightarrow GTLN:D = - 2\,khi:x = 3\\
E = 5 - 8x - {x^2}\\
= - \left( {{x^2} + 8x + 16} \right) + 16 + 5\\
= - {\left( {x + 4} \right)^2} + 21 \le 21\\
\Leftrightarrow GTLN:E = 21\,khi:x = - 4\\
B2)\\
A = {x^2} - 6x + 11\\
= {x^2} - 6x + 9 + 2\\
= {\left( {x - 3} \right)^2} + 2 \ge 2\\
\Leftrightarrow GTNN:A = 2\,khi:x = 3\\
B = {x^2} - 20x + 101\\
= {x^2} - 20x + 100 + 1\\
= {\left( {x - 10} \right)^2} + 1 \ge 1\\
\Leftrightarrow GTNN:B = 1\,khi:x = 10\\
C = {x^2} - 2x + {y^2} + 4y + 8\\
= {x^2} - 2x + 1 + {y^2} + 4y + 4 + 3\\
= {\left( {x - 1} \right)^2} + {\left( {y + 2} \right)^2} + 3 \ge 3\\
\Leftrightarrow GTNN:C = 3\,khi:\left\{ \begin{array}{l}
x = 1\\
y = - 2
\end{array} \right.
\end{array}$
