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\[\begin{array}{l} A = 4{x^2} + {y^2} + 4x + 2\\ = \left( {4{x^2} + 4x + 1} \right) + {y^2} + 1\\ = {\left( {2x + 1} \right)^2} + {y^2} + 1\\ Vi\,\,\,\left\{ \begin{array}{l} {\left( {2x + 1} \right)^2} \ge 0\,\,\,\forall x\\ {y^2} \ge 0\,\,\,\forall y \end{array} \right.\\ \Rightarrow A \ge 1.\\ Dau\,\,\, = \,\,\,xay\,\,ra \Leftrightarrow \left\{ \begin{array}{l} 2x + 1 = 0\\ y = 0 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} x = - \frac{1}{2}\\ y = 0 \end{array} \right.. \end{array}\]
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