Question

\(\left(x+3\right)^2+\left(y+5\right)^2+7\) đạt GTNN

Answer 1

Ta thấy :

\(\left(x+3\right)^2\ge0\forall x\)

\(\left(y+5\right)^2\ge0\forall y\)

\(\Rightarrow\left(x+3\right)^2+\left(y+5\right)^2\ge0\forall x,y\)

\(\Rightarrow\left(x+3\right)^2+\left(y+5\right)^2+7\ge7\)

Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}\left(x+3\right)^2=0\\\left(y+5\right)^2=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+3=0\\y+5=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=-3\\y=-5\end{matrix}\right.\)

Vậy : \(\left(x+2\right)^2+\left(x+5\right)^2+7\) đạt giá trị nhỏ nhất \(=7\Leftrightarrow x=-3,y=-5\)