$\begin{array}{l}a) \quad A = 4x^2 - 4xy + 2y^2 +1\\ \to A = 4x^2 - 4xy + y^2 + y^2 + 1\\ \to A = (2x - y)^2 + y^2 + 1\\ Ta\,\,có:\\ \begin{cases}(2x - y)^2 \geq 0,\,\forall x,y\\y^2\geq 0,\,\forall y\end{cases}\\ \to A \geq 1\\ \to \min A = 1 \Leftrightarrow \begin{cases}2x - y = 0\\y = 0\end{cases}\Leftrightarrow \begin{cases}x = 0\\y = 0\end{cases}\\ b)\quad B =10x^2 +2y^2+ 2z^2 + 6xy + 2yz + 2xz +5\\ \to B = (x^2 + 2xy + y^2 + 2yz + 2zx + z^2) + 4x^2 + 4xy + y^2 + 5x^2 + z^2 + 5\\ \to B = (x + y + z)^2 + (2x + y)^2 + 5x^2 + y^2 + 5\\ Ta\,\,có:\\ \begin{cases}(x + y + z)^2 \geq 0\\(2x + y)^2 \geq 0\\x^2 \geq 0\\z^2 \geq 0\end{cases}\\ \to B \geq 5\\ \to \min B = 5 \Leftrightarrow \begin{cases} x + y + z = 0\\2x + y = 0\\x = 0\\z = 0\end{cases}\Leftrightarrow x = y =z = 0\end{array}$
