Question

Giá trị nhỏ nhất của biểu thức A = 3x² + y² + 2xy + 4x

Answer 1

\(A=x^2+2xy+y^2+2x^2+4x+2-2\)

\(A=\left(x+y\right)^2+2\left(x+1\right)^2-2\ge-2\)

\(\Rightarrow A_{min}=-2\) khi \(\left\{{}\begin{matrix}x+1=0\\x+y=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-1\\y=1\end{matrix}\right.\)

Answer 2

\(A=\left(y^2+2xy+x^2\right)+\left(2x^2+4x+2\right)-2\)

\(A=\left(y+x\right)^2+2\left(x+1\right)^2-2\)

\(\left\{{}\begin{matrix}\left(x+y\right)^2\ge0\\\left(x+1\right)^2\ge0\end{matrix}\right.\)\(\Rightarrow A\ge-2\)

\(A_{min}=-2\) khi \(x=-1,y=1\)