$\begin{array}{l}A=x^2-2x+10\\=x^2 - 2x + 1 +9\\=(x-1)^2 + 9\\A \geq 9, \forall x\\\Rightarrow A_{min} = 9 \Leftrightarrow x - 1 = 0 \Leftrightarrow x = 1\\\\B = x^2 -3x + 8\\=x^2 -2.\dfrac{3}{2}.x+\dfrac{9}{4}+\dfrac{23}{4}\\=(x-\dfrac{3}{2})^2 +\dfrac{23}{4}\\B \geq \dfrac{23}{4}, \forall x\\\Rightarrow B_{min} = \dfrac{23}{4} \Leftrightarrow x - \dfrac{3}{2} = 0 \Leftrightarrow x = \dfrac{3}{2}\\\\C=2x^2 - 5x +7\\=2(x^2 - 2.\dfrac{5}{4}.x + \dfrac{25}{16}) +\dfrac{31}{8}\\=2(x-\dfrac{5}{4})^2 + \dfrac{31}{8}\\C \geq \dfrac{31}{8}, \forall x\\\Rightarrow C_{min} = \dfrac{31}{8} \Leftrightarrow x - \dfrac{5}{4} = 0 \Leftrightarrow x = \dfrac{5}{4}\\\\D = (x-1)^2 + (x-3)^2+5\\Đặt \, t = x - 1\\\Rightarrow D = t^2 + (t -2)^2 + 5\\=2t^2 - 4t + 9\\=2(t^2 -2t + 1) + 7\\=2(t-1)^2 + 7\\D \geq 7, \forall x\\\Rightarrow D_{min} = 7 \Leftrightarrow t - 1 = 0 \Leftrightarrow x - 2 = 0 \Leftrightarrow x = 2\\\\E = (x^2 -4x + 1)^2 - 2(x^2 - 4x) + 8\\Đặt \, t = x^2 - 4x + 1\\\Rightarrow E = t^2 - 2(t - 1) + 8\\=t^2 - 2t + 10 \, \text{(Giống A)}\\\Rightarrow E_{min} = 9 \Leftrightarrow t - 1 = 0 \Leftrightarrow x^2 - 4x = 0 \Leftrightarrow \left[\begin{array}{l}x=0\\x=4\end{array}\right.\\\\F = (x -2)^2 + 4|x - 2| + 5\\\text{Ta có:}\\\begin{cases}(x-2)^2 \geq 0, \forall x\\|x-2|\geq 0 , \forall x\end{cases}\\\Rightarrow F\geq 5, \forall x\\\Rightarrow F_{min} = 5 \Leftrightarrow x - 2 = 0 \Leftrightarrow x = 2\\\\G = x^2 -2xy + 2y^2 + 10 y + 50\\=(x^2 -2xy + y^2) + (y^2 +2.5y + 25) + 25\\=(x-y)^2 + (y+5)^2 + 25\\G \geq 25, \forall x\\\Rightarrow G_{min} = 25 \Leftrightarrow \begin{cases}x - y = 0\\y + 5 = 0 \end{cases}\Leftrightarrow x = y = -5\\\\H = x^2 -2xy + 5y^2 - 4y + 3\\=(x^2 -2xy + y^2) + (4y^2 - 4y + 1) + 2\\=(x - y)^2 + (2y - 1)^2 + 2\\H \geq 2, \forall x\\\Rightarrow H_{min} = 2 \Leftrightarrow \begin{cases}x - y = 0\\2y - 1 = 0 \end{cases}\Leftrightarrow x = y = \dfrac{1}{2}\end{array}$
