\(\Leftrightarrow\left(x^2+y^2\right)^3+x^2+y^2+3\left(x+1\right)^2-2=0\)
\(\Leftrightarrow\left(x^2+y^2\right)^3+x^2+y^2=2-3\left(x+1\right)^2\le2\)
Đặt \(t=x^2+y^2>0\Rightarrow t^3+t\le2\)
\(\Leftrightarrow t^3+t-2\le0\)
\(\Leftrightarrow\left(t-1\right)\left(t^2+t+2\right)\le0\)
\(\Leftrightarrow t-1\le0\Rightarrow t\le1\)
\(\Rightarrow t_{max}=1\) khi \(\left\{{}\begin{matrix}x=-1\\y=0\end{matrix}\right.\)
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