\(42-3\left|y-3\right|=4\left(2012-x\right)^4\)
\(\Leftrightarrow42-3\left|y-3\right|-4\left(2012-x\right)^4=0\)
Ta thấy: \(\left\{{}\begin{matrix}\left(2012-x\right)^4\ge0\forall x\\\left|y-3\right|\ge0\forall y\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}4\left(2012-x\right)^4\ge0\forall x\\3\left|y-3\right|\ge0\forall y\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}-4\left(2012-x\right)^4\le0\forall x\\-3\left|y-3\right|\le0\forall y\end{matrix}\right.\)
\(\Rightarrow-3\left|y-3\right|-4\left(2012-x\right)^4\le0\forall x,y\)
\(\Rightarrow42-3\left|y-3\right|-4\left(2012-x\right)^4\le42\forall x,y\)
Xảy ra khi và chỉ khi \(\Rightarrow\left\{{}\begin{matrix}-4\left(2012-x\right)^4=0\\-3\left|y-3\right|=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}2012-x=0\\y-3=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=2012\\y=3\end{matrix}\right.\)
Vậy \(\left\{{}\begin{matrix}x=2012\\y=3\end{matrix}\right.\) thì thỏa mãn
