Question

Tìm GTNN của biểu thức A=x²-6y+2xy+2y²+2030

Answer 1

\(A=\left(x^2+2xy+y^2\right)+\left(y^2-6y+9\right)+2021\\ A=\left(x+y\right)^2+\left(y-3\right)^2+2021\ge2021\\ A_{min}=2021\Leftrightarrow\left\{{}\begin{matrix}x=-y=-3\\y=3\end{matrix}\right.\)

Answer 2

A=(x2+2xy+y2)+(y2−6y+9)+2021A=(x+y)2+(y−3)2+2021≥2021Amin=2021⇔{x=−y=−3y=3