ĐKXĐ: \(\left\{{}\begin{matrix}x\ge1\\y\ge2\\z\ge3\end{matrix}\right.\)
\(P=\frac{\sqrt{x-1}}{x}+\frac{\sqrt{y-2}}{y}+\frac{\sqrt{z-3}}{z}=\frac{1.\sqrt{x-1}}{x}+\frac{\sqrt{2}.\sqrt{y-2}}{\sqrt{2}y}+\frac{\sqrt{3}.\sqrt{z-3}}{\sqrt{3}z}\)
\(\Rightarrow P\le\frac{1+x-1}{2x}+\frac{2+y-2}{2\sqrt{2}y}+\frac{3+z-3}{2\sqrt{3}z}=\frac{1}{2}+\frac{1}{2\sqrt{2}}+\frac{1}{2\sqrt{3}}\)
Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}x-1=1\\y-2=2\\z-3=3\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=2\\y=4\\z=6\end{matrix}\right.\)
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