Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
A = \left( {x - 2} \right)\left( {x - 5} \right)\left( {{x^2} - 7x - 10} \right)\\
= \left( {{x^2} - 7x + 10} \right)\left( {{x^2} - 7x - 10} \right)\\
= \left[ {\left( {{x^2} - 7x} \right) + 10} \right]\left[ {\left( {{x^2} - 7x} \right) - 10} \right]\\
= {\left( {{x^2} - 7x} \right)^2} - {10^2} = {\left( {{x^2} - 7x} \right)^2} - 100 \ge - 100,\,\,\,\forall x\\
\Rightarrow {A_{\min }} = - 100 \Leftrightarrow {\left( {{x^2} - 7x} \right)^2} = 0 \Leftrightarrow x\left( {x - 7} \right) = 0 \Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = 7
\end{array} \right.\\
B = 5{x^2} + 2{y^2} + 4xy - 2x + 4y + 2023\\
= \left( {4{x^2} + 4xy + {y^2}} \right) + \left( {{x^2} - 2x + 1} \right) + \left( {{y^2} + 4y + 4} \right) + 2018\\
= {\left( {2x + y} \right)^2} + {\left( {x - 1} \right)^2} + {\left( {y + 2} \right)^2} + 2018 \ge 2018,\,\,\,\,\forall x,y\\
\Rightarrow {B_{\min }} = 2018 \Leftrightarrow \left\{ \begin{array}{l}
{\left( {2x + y} \right)^2} = 0\\
{\left( {x - 1} \right)^2} = 0\\
{\left( {y + 2} \right)^2} = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = 1\\
y = - 2
\end{array} \right.
\end{array}\)
Đề câu c có nhầm không em?
