a) \(C=3\left(x^2-\dfrac{4}{3}x+\dfrac{1}{3}\right)=3\left(x^2-2\cdot\dfrac{2}{3}x+\dfrac{4}{9}-\dfrac{4}{9}+\dfrac{1}{3}\right)=3\left[\left(x-\dfrac{2}{3}\right)^2-\dfrac{1}{9}\right]=3\left(x-\dfrac{2}{3}\right)^2-\dfrac{1}{3}\ge-\dfrac{1}{3}\)
C đạt GTNN khi và chỉ khi: \(x-\dfrac{2}{3}=0\Leftrightarrow x=\dfrac{2}{3}\)
Kl: \(Min_C=-\dfrac{1}{3}\Leftrightarrow x=\dfrac{2}{3}\)
b) \(D=\left(x^2-6xy+9y^2\right)+\left(y^2-4y+4\right)+8=\left(x-3y\right)^2+\left(y-2\right)^2+8\ge8\)
D đạt GTNN khi và chỉ khi: \(\left\{{}\begin{matrix}x-3y=0\\y-2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=6\\y=2\end{matrix}\right.\)
KL: \(Min_D=8\Leftrightarrow\left\{{}\begin{matrix}x=6\\y=2\end{matrix}\right.\)