Có: \(\left|x+\frac{17}{3}\right|+\left|y-\frac{2000}{1999}\right|+\left|z-2005\right|=0\)
\(\Rightarrow\left[\begin{matrix}\left|x+\frac{17}{3}\right|=0\\\left|y-\frac{2000}{1999}\right|=0\\\left|z-2005\right|=0\end{matrix}\right.\)
\(\Rightarrow\left[\begin{matrix}x=\frac{-17}{3}\\y=\frac{2000}{1999}\\z=2005\end{matrix}\right.\)
\(\Rightarrow x+z=\frac{-17}{3}+2005=\frac{5998}{3}\)
Vậy............
Vì \(\left|x+\frac{17}{3}\right|\ge0;\left|y-\frac{2000}{1999}\right|\ge0;\left|z-2005\right|\ge0\)
\(\Rightarrow\left|x+\frac{17}{3}\right|+\left|y-\frac{2000}{1999}\right|+\left|z-2005\right|\ge0\)
Dấu "=" xảy ra khi \(\left\{\begin{matrix}\left|x+\frac{17}{3}\right|=0\\\left|y-\frac{2000}{1999}\right|=0\\\left|z-2005\right|=0\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=\frac{-17}{3}\\y=\frac{2000}{1999}\\z=2005\end{matrix}\right.\)
\(\Rightarrow x+z=\frac{-17}{3}+2005=\frac{5998}{3}\)
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