\(\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{2}\)
\(\Rightarrow\dfrac{x^3}{3^3}=\dfrac{y^3}{4^3}=\dfrac{z^3}{2^3}=\dfrac{x^3-y^3+z^3}{3^3-4^3+2^3}=\dfrac{-29}{27-64+8}=1\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x^3}{3^3}=1\\\dfrac{y^3}{4^3}=1\\\dfrac{z^3}{2^3}=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x^3=3^3\\y^3=4^3\\z^3=2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=3\\y=4\\z=2\end{matrix}\right.\)
\(\Rightarrow x-y+z=3-4+2=1\)
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