a) \(A=\left(x^2+3x+\dfrac{9}{4}\right)-\dfrac{5}{4}=\left(x+\dfrac{3}{2}\right)^2-\dfrac{5}{4}\ge-\dfrac{5}{4}\)
\(minA=-\dfrac{5}{4}\Leftrightarrow x=-\dfrac{3}{2}\)
b) \(B=\left(x^2+2xy+y^2\right)+\left(x^2+6x+9\right)+3=\left(x+y\right)^2+\left(x+3\right)^2+3\ge3\)
\(minB=3\Leftrightarrow\left\{{}\begin{matrix}x=-3\\y=3\end{matrix}\right.\)
c) \(C=2x-x^2=-\left(x^2-2x+1\right)+1=-\left(x-1\right)^2+1\le1\)
\(maxC=1\Leftrightarrow x=1\)
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