Ta có: \(\left\{{}\begin{matrix}\left|3x-5\right|\ge0\\\left(2y+5\right)^{208}\ge0\\\left(4z-3\right)^{20}\ge0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}3x-5=0\\2y+5=0\\4z-3=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{5}{3}\\y=-\dfrac{5}{2}\\z=\dfrac{3}{4}\end{matrix}\right.\)
Vì \(\left|3x-5\right|+\left(2y+5\right)^{208}+\left(4z-3\right)^{20}\ge0\)
Do đó đề xảy ra khi \(\left|3x-5\right|+\left(2y+5\right)^{208}+\left(4z-3\right)^{20}=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x-5=0\\2y+5=0\\4z-3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{3}\\y=-\dfrac{5}{2}\\z=\dfrac{3}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x-5=0\\2y+5=0\\4z-3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{3}\\y=-\dfrac{5}{2}\\z=\dfrac{3}{4}\end{matrix}\right.\)
