\(a.A=x^2+4x+1=\left(x^2+4x+4\right)-3=\left(x+2\right)^2-3\ge-3\Leftrightarrow Min_A=-3\Rightarrow x=-2\)\(b.B=x^2-10x+16=\left(x^2-10x+25\right)-9=\left(x-5\right)^2-9\ge-9\Rightarrow Min_B=-9\Leftrightarrow x=5\)\(C=x^2+5x-6=\left(x^2+2.x.\dfrac{5}{2}+\dfrac{25}{4}\right)-\dfrac{49}{4}=\left(x+\dfrac{5}{2}\right)^2-\dfrac{49}{4}\ge-\dfrac{49}{4}\Rightarrow Min_C=-\dfrac{49}{4}\Leftrightarrow x=-\dfrac{5}{2}\)\(d.D=x^2-x+1=\left(x^2-2.x.\dfrac{1}{2}+\dfrac{1}{4}\right)+\dfrac{3}{4}=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\Rightarrow Min=\dfrac{3}{4}\Leftrightarrow x=\dfrac{1}{2}\)\(e.E=x^2+x+2=\left(x+\dfrac{1}{2}\right)^2+\dfrac{7}{4}\ge\dfrac{7}{4}\Rightarrow Min_E=\dfrac{7}{4}\Leftrightarrow x=-\dfrac{1}{2}\)
