ĐKXĐ: \(x\ge0\)
\(P=1-\frac{3}{\sqrt{x}+1}\)
Để \(P\in Z\Leftrightarrow\frac{3}{\sqrt{x}+1}\in Z\Rightarrow\sqrt{x}+1=Ư\left(3\right)\)
Mà \(\sqrt{x}+1\ge1\Rightarrow\sqrt{x}+1=\left\{1;3\right\}\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt{x}+1=1\\\sqrt{x}+1=3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\)
b/ \(\sqrt{x}\ge0\Rightarrow\frac{3}{\sqrt{x}+1}\le3\Rightarrow P=1-\frac{3}{\sqrt{x}+1}\ge1-3=-2\)
\(P_{min}=-2\) khi \(x=0\)