Question

Tính GTNN của biểu thức M=\(x^2+y^2-xy-x+y+1\)

Answer 1

\(M=x^2+\frac{y^2}{4}+\frac{1}{4}-xy-x+\frac{y}{2}+\frac{3y^2}{4}+\frac{y}{2}+\frac{3}{4}\)

\(M=\left(x-\frac{y}{2}-\frac{1}{2}\right)^2+\frac{3}{4}\left(y+1\right)^2\ge0\)

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