Question

[Trần Băng Băng]

BT1: Tìm GTNN a) A=x^2-4xy+5y^2+10x-22y+2017 b) B=x^2+y^2-xy-x+y+1 GIÚP MÌNH VỚI NHA THỨ 6 MÌNH PHẢI NỘP RỒI

Answer 1

[diem ngo]

A=x^2-4xy+5y^2+10x-22y+2017

\(x^2-4xy+4y^2+y^2-2y+1+10\left(x-2y\right)+2016\)=\(\left(x-2y\right)^2+10\left(x-2y\right)+25+\left(y-1\right)^2+2011\)

=\(\left(x-2y+5\right)^2+\left(y-1\right)^2+2011\ge2011\)

=>minA=2011

dau "=" xay ra <=> \(\left\{\begin{matrix}x-2y+5=0\\y=1\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=-3\\y=1\end{matrix}\right.\)

Answer 2

[diem ngo]

B=\(x^2+y^2-xy-x-y+1\)

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

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

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