ĐKXĐ: y>=0
\(\left(x+1\right)^{2024}>=0\forall x\)
\(\left(\sqrt{y-1}\right)^{2023}>=0\forall y\) thỏa mãn ĐKXĐ
=>\(\left(x+1\right)^{2024}+\left(\sqrt{y-1}\right)^{2023}>=0\forall x,y\) thỏa mãn ĐKXĐ
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x+1=0\\y-1=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-1\\y=1\end{matrix}\right.\)