Đáp án:
Giải thích các bước giải:
\[\begin{array}{l}A = 2{x^2} - 8x + 1\\ = 2.\left( {{x^2} - 2.2x + 4} \right) + 1 - 8\\ = 2.{\left( {x - 2} \right)^2} - 7 \ge - 7\\ \Rightarrow \min A = - 7 \Leftrightarrow x = 2\\B = {x^2} + 6x + 12\\ = {x^2} + 2.3x + 9 + 3\\ = {\left( {x + 3} \right)^2} + 3 \ge 3\\ \Rightarrow \min B = 3 \Leftrightarrow x = - 3\\C = {x^2} - x\\ = {x^2} - 2.\frac{1}{2}.x + \frac{1}{4} - \frac{1}{4}\\ = {\left( {x - \frac{1}{2}} \right)^2} - \frac{1}{4} \le \frac{{ - 1}}{4}\\ \Rightarrow \min C = \frac{{ - 1}}{4} \Leftrightarrow x = \frac{1}{2}\\D = {x^2} + 5x - 2\\ = {x^2} - 2.\frac{5}{2}.x + \frac{{25}}{4} - \frac{{25}}{4} - 2\\ = {\left( {x - \frac{5}{2}} \right)^2} - \frac{{33}}{4} \le \frac{{ - 33}}{4}\\ \Rightarrow \min D = \frac{{ - 33}}{4} \Leftrightarrow x = \frac{5}{2}\end{array}\]
