\(A=4-5x^2-y^2+2xy-4x\)
\(=5-1-x^2-4x^2-y^2+2xy-4x\)
\(=5-(1+4x+4x^2)-(x^2-2xy+y^2)\)
\(=5-(1+2x)^2-(x-y)^2\)
Do \((1+2x)^2\geq 0\forall x\in\mathbb{R}\)
\((x-y)^2\geq 0\forall x\in\mathbb{R}\)
\(\Rightarrow 5-(1+2x)^2-(x-y)^2\leq 5\forall x\in\mathbb{R}\)
Vậy \(A_{max}=5\Leftrightarrow 1+2x=0\Rightarrow x=-\dfrac{1}{2}\Rightarrow x-y=0\Rightarrow y=-\dfrac{1}{2}\)
