Ta có :
\(\left(2x-5\right)^{2000}\ge0\forall x\)
\(\left(3y+4\right)^{2002}\ge0\forall y\)
\(\Rightarrow\left(2x-5\right)^{2000}+\left(3y+4\right)^{2002}\ge0\forall x;y\)
Mà theo GT : \(\left(2x-5\right)^{2000}+\left(3y+4\right)^{2002}\le0\)
\(\Rightarrow\left(2x-5\right)^{2000}+\left(3y+4\right)^{2002}=0\)
Dấu \("="\) xảy ra
\(\Leftrightarrow\left\{{}\begin{matrix}\left(2x-5\right)^{2000}=0\\\left(3y+4\right)^{2002}=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-5=0\\3y+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x=5\\3y=-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}\\y=-\dfrac{4}{3}\end{matrix}\right.\)
Vậy \(x=\dfrac{5}{2};y=-\dfrac{4}{3}\)
