\(\Leftrightarrow\left\{{}\begin{matrix}x^2-2x+1+y^2=1\\\left(x-1\right)^3+y^3=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-1\right)^2+y^2=1\\\left(x-1\right)^3+y^3=1\end{matrix}\right.\)
Do \(\left(x-1\right)^2+y^2=1\Rightarrow\left\{{}\begin{matrix}\left|x-1\right|\le1\\\left|y\right|\le1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left(x-1\right)^3\le\left(x-1\right)^2\\y^3\le y^2\end{matrix}\right.\) \(\Rightarrow\left(x-1\right)^3+y^3\le\left(x-1\right)^2+y^2=1\)
Dấu "=" xảy ra khi và chỉ khi \(\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1=0\\y=1\end{matrix}\right.\\\left\{{}\begin{matrix}x-1=1\\y=0\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left(x;y\right)=\left(1;1\right);\left(2;0\right)\)
