Tìm GTNN của các biểu thức: Q = 2x^2 - 6x

* Hướng dẫn giải

$$\begin{gathered} \mathrm{Q}=2{\mathrm{x}}^2-6\mathrm{x}=2\left({\mathrm{x}}^2-2.\mathrm{x}.\frac{3}{2}+\frac{9}{4}-\frac{9}{4}\right)=2{\left(\mathrm{x}-\frac{3}{2}\right)}^2-\frac{9}{2} \\ \mathrm{Vì} 2{\left(\mathrm{x}-\frac{3}{2}\right)}^2\ge 0\left(\forall \mathrm{x}\right)\Rightarrow 2{\left(\mathrm{x}-\frac{3}{2}\right)}^2-\frac{9}{2}\ge -\frac{9}{2} (\mathrm{với} \mathrm{mọi} \mathrm{x}) \\ \mathrm{Dấu} \text{'}\text{'}=\text{'}\text{'} \mathrm{xảy} \mathrm{ra} \mathrm{khi} \mathrm{và} \mathrm{chỉ} \mathrm{khi} \mathrm{x}=\frac{3}{2} \\ \mathrm{Vậy} \mathrm{MinQ}=-\frac{9}{2}\iff \mathrm{x}=\frac{3}{2} \end{gathered}$$