`a)`\(A=x^2+6x+2\)
\(A=\left(x^2+6x+9\right)-9+2\)
\(A=\left(x+3\right)^2-7\ge-7\)
Dấu "=" xảy ra khi \(x=-3\)
Vậy \(Min_A=-7\) khi \(x=-3\)
`b)`\(B=-x^2+5x+2\)
\(B=-\left(x^2+5x+\dfrac{25}{4}\right)+\dfrac{25}{4}+2\)
\(B=-\left(x+\dfrac{5}{2}\right)^2+\dfrac{33}{4}\le\dfrac{33}{4}\)
Dấu "=" xảy ra khi \(x=-\dfrac{5}{2}\)
Vậy \(Max_B=-\dfrac{5}{2}\) khi \(x=-\dfrac{5}{2}\)
`c)`\(C=x^4-2x^2+4\)
\(C=\left(x^4-2x^2+1\right)+3\)
\(C=\left(x^2-1\right)^2+3\ge3\)
Dấu "=" xảy ra khi \(x=\pm1\)
Vậy \(Min_C=3\) khi \(x=\pm1\)
\(D=x^2+2x\left(y+2\right)+2y^2+6y+10=x^2+2x\left(y+2\right)+\left(y+2\right)^2+y^2+2y+1+5=\left(x+y+2\right)^2+\left(y+1\right)^2+5\ge5\)
\(dấu"="\Leftrightarrow\left\{{}\begin{matrix}y=-1\\x+y+2=0\end{matrix}\right.\)\(\Leftrightarrow x=y=-1\)
