Câu hỏi của Rồng Đom Đóm

Question

Tìm GTNN của $A=2x^2+3y^2+4xy-8x-2y+18$

Phạm Nguyễn Tất Đạt · Accepted Answer

Ta có:$A=2x^2+3y^2+4xy-8x-2y+18$

$A=2\left(x^2+2xy+y^2\right)-8\left(x+y\right)+8+y^2+6y+9+1$

$A=2\left[\left(x+y\right)^2-4\left(x+y\right)+4\right]+\left(y+3\right)^2+1$

$A=2\left(x+y-2\right)^2+\left(y+3\right)^2+1\ge1$

$\Rightarrow MINA=1\Leftrightarrow\left\{{}\begin{matrix}x=5\y=-3\end{matrix}\right.$Câu trả lời: Ta có:$A=2x^2+3y^2+4xy-8x-2y+18$

$A=2\left(x^2+2xy+y^2\right)-8\left(x+y\right)+8+y^2+6y+9+1$

$A=2\left[\left(x+y\right)^2-4\left(x+y\right)+4\right]+\left(y+3\right)^2+1$

$A=2\left(x+y-2\right)^2+\left(y+3\right)^2+1\ge1$

$\Rightarrow MINA=1\Leftrightarrow\left\{{}\begin{matrix}x=5\y=-3\end{matrix}\right.$

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