Bài giải
\(\left|3x-5\right|+\left(2y+5\right)^{2008}+\left(4z-3\right)^{2006}\le0\)
Mà \(\hept{\begin{cases}\left|3x-5\right|\ge0\\\left(2y+5\right)^{2008}\ge0\\\left(4z-3\right)^{2006}\ge0\end{cases}}\) \(\Rightarrow\) Chỉ xảy ra trường hợp : \(\left|3x-5\right|+\left(2y+5\right)^{2008}+\left(4z-3\right)^{2006}=0\)
\(\Rightarrow\hept{\begin{cases}\left|3x-5\right|=0\\\left(2y+5\right)^{2008}=0\\\left(4z-3\right)^{2006}=0\end{cases}}\) \(\Rightarrow\hept{\begin{cases}3x-5=0\\2y+5=0\\4z-3=0\end{cases}}\) \(\Rightarrow\hept{\begin{cases}3x=5\\2y=-5\\4z=3\end{cases}}\) \(\Rightarrow\hept{\begin{cases}x=\frac{5}{3}\\y=-\frac{5}{2}\\x=\frac{3}{4}\end{cases}}\)
\(\Rightarrow\text{ }x=\frac{5}{3}\text{ , }y=-\frac{5}{2}\text{ , }z=\frac{3}{4}\)