\(A=x^2-4xy+7y^2+10x-24y+30\\ =\left(x^2-4xy+4y^2\right)+10\left(x-y\right)+25+\left(3y^2-14y+\dfrac{49}{3}\right)-\dfrac{34}{3}\\ =\left(x-2y+5\right)^2+3\left(y-\dfrac{7}{3}\right)^2-\dfrac{34}{5}\)
Với mọi x;y thì \(\left(x-2y+5\right)^2\ge0;3\left(y-\dfrac{7}{3}\right)^2\ge0\)
Do đó:\(A\ge-\dfrac{34}{5}\)
Để \(A=-\dfrac{34}{5}\) thì:
\(\left[{}\begin{matrix}\left(x-2y+5\right)^2=0\\\left(y-\dfrac{7}{3}\right)^2=0\\\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-2y=-5\\y=\dfrac{7}{3}\\\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5+\dfrac{2.7}{3}=-\dfrac{1}{3}\\y=\dfrac{7}{3}\\\end{matrix}\right.\)
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