Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
A = \left( {x - 1} \right)\left( {x - 4} \right)\left( {x - 5} \right)\left( {x - 8} \right) + 2001\\
= \left[ {\left( {x - 1} \right)\left( {x - 8} \right)} \right].\left[ {\left( {x - 4} \right)\left( {x - 5} \right)} \right] + 2001\\
= \left( {{x^2} - 9x + 8} \right)\left( {{x^2} - 9x + 20} \right) + 2001\\
= \left[ {\left( {{x^2} - 9x + 14} \right) - 6} \right].\left[ {\left( {{x^2} - 9x + 14} \right) + 6} \right] + 2001\\
= {\left( {{x^2} - 9x + 14} \right)^2} - {6^2} + 2001\\
= {\left( {{x^2} - 9x + 14} \right)^2} + 1965\\
{\left( {{x^2} - 9x + 14} \right)^2} \ge 0,\,\,\,\forall x\\
\Rightarrow {\left( {{x^2} - 9x + 14} \right)^2} + 1965 \ge 1965,\,\,\,\,\forall x\\
\Rightarrow A \ge 1965,\,\,\,\forall x\\
\Rightarrow {A_{\min }} = 1965 \Leftrightarrow {\left( {{x^2} - 9x + 14} \right)^2} = 0 \Leftrightarrow {x^2} - 9x + 14 = 0\\
\Leftrightarrow \left( {x - 2} \right)\left( {x - 7} \right) = 0 \Leftrightarrow \left[ \begin{array}{l}
x = 2\\
x = 7
\end{array} \right.
\end{array}\)
