$A=x^2+7x+13=(2x)^2+2.2x.\dfrac{7}{4}+\dfrac{49}{16}+\dfrac{159}{16}=(2x+\dfrac{7}{4})^2+\dfrac{159}{16}$
Vậy $A_{min}=\dfrac{159}{16}$ khi $2x+\dfrac{7}{4}=0$ hay $x=\dfrac{-7}{8}$
$B=5-8x+x^2=16-8x+x^2-11=(4-x)^2-11$
Vậy $B_{min}=-11$ khi $4-x=0$ hay $x=4$
$C=(x-1)(x+2)(x+3)(x+6)\\=(x-1)(x+6)(x+2)(x+3)\\=(x^2+5x-6)(x^2+5x+6)\\=(x^2+5x)^2-36$
Vậy $C_{min}=-36$ khi $x^2+5x=0$ hay $x=\{0;-5\}$
$f(x,y)=x^2+y^2-6x+5y+1\\=x^2-6x+9+y^2+5y+\dfrac{25}{4}-\dfrac{57}{4}\\=(x-3)^2+(y+\dfrac{5}{2})^2-\dfrac{57}{4}$
Vậy $f(x,y)_{min}=-\dfrac{57}{4}$ khi $x-3=0\ ;\ y+\dfrac{5}{2}=0$ hay $(x;y)=(3;\dfrac{-5}{2})$
$g(x,y)=5x^2+y^2+10+4xy+14x-6y\\=4x^2+14x+49+y^2-6y+9+x^2+4xy+2y^2-2y^2-48\\=(2x+7)^2+(y-3)^2+(x+2y)^2-(2y^2+48)$
