Đáp án:
\(Min\,\,A = 10\,\,\,khi\,\,\,x = \frac{1}{5};\,\,y = 1.\)
Giải thích các bước giải:
\[\begin{array}{l}
A = 25{x^2} + 3{y^2} - 10x + 11\\
= \left( {25{x^2} - 10x + 1} \right) + 3{y^2} + 10\\
= {\left( {5x - 1} \right)^2} + 3{y^2} + 10\\
Vi\,\,\,\left\{ \begin{array}{l}
{\left( {5x - 1} \right)^2} \ge 0\,\,\forall x\\
3{y^2} \ge 0\,\,\forall y
\end{array} \right.\\
\Rightarrow A = {\left( {5x - 1} \right)^2} + 3{y^2} + 10 \ge 10\\
Dau\,\,\, = \,\,xay\,\,ra \Leftrightarrow \left\{ \begin{array}{l}
5x - 1 = 0\\
y = 1
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = \frac{1}{5}\\
y = 1
\end{array} \right..\\
Vay\,\,\,Min\,\,A = 10\,\,\,khi\,\,\,x = \frac{1}{5};\,\,y = 1.
\end{array}\]
