Tìm GTNN của 2x^2 - 3x + 5

$\displaystyle  \begin{array}{{>{\displaystyle}l}}
\ \ \ \ 2x^{2} -3x+5\\
\ =2.\left( x^{2} -\frac{3}{2} x+\frac{5}{2}\right)\\
=2.\left[ x^{2} -2.x.\frac{3}{4} +\left(\frac{3}{4}\right)^{2} -\left(\frac{3}{4}\right)^{2} +\frac{5}{2}\right]\\
=2.\left[\left( x-\frac{3}{4}\right)^{2} +\frac{31}{16}\right]\\
=2.\left( x-\frac{3}{4}\right)^{2} +\frac{31}{8}
\end{array}$
Nhận xét
$\displaystyle  \begin{array}{{>{\displaystyle}l}}
2.\left( x-\frac{3}{4}\right)^{2} \geqslant 0\ \forall x\\
\Rightarrow 2.\left( x-\frac{3}{4}\right)^{2} +\frac{31}{8} \geqslant \frac{31}{8} \ \ \forall x\\
\Rightarrow min\left( 2x^{2} -3x+5\right) =\frac{31}{8}
\end{array}$
Xảy ra khi $\displaystyle x=\frac{3}{4}$