Vì \(\left(x-17\right)^4\ge0\forall x;\left|y+42\right|\ge0\forall y\)
\(\Rightarrow A\ge2018\forall x;y\)
Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}x-17=0\\y+42=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=17\\y=-42\end{cases}}}\)
Vậy..........
\(A=\left(x-17\right)^4+\left|y+42\right|+2018\)
Vì \(\left(x-17\right)^4\ge0vs\forall x;\left|y+42\right|\ge0vs\forall y\)
\(\Rightarrow A\ge2018vs\forall x;y\)
Dấu \(''=''\) xảy ra khi : \(\left(x-17\right)^4+\left|y+42\right|=0\)
\(\Rightarrow\hept{\begin{cases}\left(x-17\right)^4=0\\\left|y+42\right|=0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x-17=0\\y+42=0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=17\\y=-42\end{cases}}\)
Vậy \(A_{min}=2018\Leftrightarrow x=17;y=-42\)
