\(\left|3x-5\right|+\left(2y+5\right)^{208}+\left(4z-3\right)^{20}\le0\)\(\left(1\right)\)
Mà \(\left\{{}\begin{matrix}\left|3x-5\right|\ge0\\\left(2y+5\right)^{208}\ge0\\\left(4z-3\right)^{20}\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left|3x-5\right|+\left(2y+5\right)^{208}+\left(4z-3\right)^{20}\ge0\left(2\right)\)
Từ \(\left(1\right)+\left(2\right)\Leftrightarrow\left|3x-5\right|+\left(2y+5\right)^{208}+\left(4z-3\right)^{20}=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left|3x-5\right|=0\\\left(2y+5\right)^{208}=0\\\left(4z-3\right)^{20}=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}3x-5=0\\2y+5=0\\4z-3=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{3}\\y=\dfrac{-5}{2}\\x=\dfrac{3}{4}\end{matrix}\right.\)
Vaayj ....