b.
\(4B=12x^2+12y^2+4z^2+20xy-12yz-12zx-8x-8y+12\)
\(=\left(9x^2+9y^2+4z^2+18xy-12yz-12zx\right)+\left(x^2+y^2+2xy\right)-4\left(x+y\right)+4+2\left(x^2-2x+1\right)+2\left(y^2-2y+1\right)+4\)
\(=\left(3x+3y-2z\right)^2+\left(x+y\right)^2-4\left(x+y\right)+4+2\left(x-1\right)^2+2\left(y-1\right)^2+4\)
\(=\left(3x+3y-2z\right)^2+\left(x+y-2\right)^2+2\left(x-1\right)^2+2\left(y-1\right)^2+4\ge4\)
\(\Rightarrow B\ge1\)
Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}x=1\\y=1\\z=3\end{matrix}\right.\)
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