Đáp án:

Giải thích các bước giải: \(\begin{array}{l}A = 4{x^2} + 4x + 11\\A = {\left( {2x} \right)^2} + 2.2x + 1 + 10\\A = {\left( {2x + 1} \right)^2} + 10 \ge 10\\{A_{\min }} = 10 \Leftrightarrow {\left( {2x + 1} \right)^2} = 0 \Leftrightarrow 2x + 1 = 0 \Leftrightarrow x = \frac{{ - 1}}{2}\end{array}\) \(\begin{array}{l}B = {x^2} - 8\,x + 5\\B = {x^2} - 2.x.4 + {4^2} - 11\\B = \,{\left( {x - 4} \right)^2} - 11 \ge - 11\\ \Rightarrow {B_{\min }} = - 11 \Leftrightarrow {\left( {x - 4} \right)^2} = 0 \Rightarrow x = 4\end{array}\) \(\begin{array}{l}C = {x^2} + x + 1\\C = {x^2} + 2.\frac{1}{2}.x + {\left( {\frac{1}{2}} \right)^2} - {\left( {\frac{1}{2}} \right)^2} + 1\\C = {\left( {x + \frac{1}{2}} \right)^2} + \frac{3}{4} \ge \frac{3}{4}\\ \Rightarrow {C_{\min }} = \frac{3}{4} \Leftrightarrow {\left( {x + \frac{1}{2}} \right)^2} = 0 \Leftrightarrow x = \frac{{ - 1}}{2}\end{array}\) \(\begin{array}{l}D = 4{x^2} + 4x + 2\\D = {\left( {2x} \right)^2} + 2.2x + 1 + 1\\D = {\left( {2x + 1} \right)^2} + 1 \ge 1\\{D_{\min }} = 1 \Leftrightarrow {\left( {2x + 1} \right)^2} = 0 \Leftrightarrow x = \frac{{ - 1}}{2}\end{array}\) \(\begin{array}{l}E = {x^2} - 4x + 24\\E = {x^2} - 2.2.x + 4 + 20\\E = {\left( {x - 2} \right)^2} + 20 \ge 20\\ \Rightarrow {E_{\min }} = 20 \Leftrightarrow {\left( {x - 2} \right)^2} = 0 \Leftrightarrow x = 2\end{array}\) \(\begin{array}{l}F = 3{x^2} + 2x + 1\\F = 3\left( {{x^2} + 2.\frac{1}{3}x + \frac{1}{9}} \right) + \frac{2}{3}\\F = 3.{\left( {x + \frac{1}{3}} \right)^2} + \frac{2}{3} \ge \frac{2}{3}\\ \Rightarrow {F_{\min }} = \frac{2}{3} \Leftrightarrow {\left( {x + \frac{1}{3}} \right)^2} = 0 \Leftrightarrow x = \frac{{ - 1}}{3}\end{array}\)