Đáp án+Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} Có\ A=\ 2x^{2} +2x+3\\ \ \ \ \ \ \ \ \ \ =2x^{2} +2x+\frac{1}{2} +\frac{5}{2}\\ \ \ \ \ \ \ \ \ \ =2\left( x^{2} +x+\frac{1}{4}\right) +\frac{5}{2}\\ \ \ \ \ \ \ \ \ \ =2\left( x+\frac{1}{2}\right)^{2} +\frac{5}{2}\\ Vì\left( x+\frac{1}{2}\right)^{2} \geqslant 0\ mọi\ x\\ \Leftrightarrow 2\left( x+\frac{1}{2}\right)^{2} \geqslant 0\ mọi\ x\\ \Leftrightarrow 2\left( x+\frac{1}{2}\right)^{2} +\frac{5}{2} \ \geqslant \frac{5}{2} \ mọi\ x\\ \Leftrightarrow A\geqslant \frac{5}{2} \ mọi\ x\\ Dấu"="\ xảy\ ra\Leftrightarrow x+\frac{1}{2} =0\Leftrightarrow x=-\frac{1}{2}\\ \\ Vậy\ Min\ A=\frac{5}{2} \ khi\ x=-\frac{1}{2} \end{array}$
