1: P<0
=>\(\dfrac{\sqrt{x}-3}{\sqrt{x}+2}< 0\)
=>\(\sqrt{x}-3< 0\)
=>\(\sqrt{x}< 3\)
=>0<x<9
2: P<0
=>0<x<9
mà x là số nguyên dương
nên \(x\in\left\{1;2;3;...;8\right\}\)
3: |P|=P
=>P<=0
=>\(\sqrt{x}-3< =0\)
=>\(\sqrt{x}< =3\)
=>0<x<=9
4: P>4/9
=>\(\dfrac{\sqrt{x}-3}{\sqrt{x}+2}>\dfrac{4}{9}\)
=>\(\dfrac{9\left(\sqrt{x}-3\right)-4\left(\sqrt{x}+2\right)}{9\left(\sqrt{x}+2\right)}>0\)
=>\(9\left(\sqrt{x}-3\right)-4\left(\sqrt{x}+2\right)>0\)
=>\(5\sqrt{x}-35>0\)
=>\(\sqrt{x}>7\)
=>x>49
5: Để \(\sqrt{P}\) có nghĩa thì P>=0
=>\(\dfrac{\sqrt{x}-3}{\sqrt{x}+2}>=0\)
=>\(\sqrt{x}-3>=0\)
=>x>=9
\(\sqrt{P}< \dfrac{2}{3}\)
=>\(0< =P< \dfrac{4}{9}\)
=>\(\left\{{}\begin{matrix}P>=0\\P-\dfrac{4}{9}< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=9\\\dfrac{9\left(\sqrt{x}-3\right)-4\left(\sqrt{x}+2\right)}{9\left(\sqrt{x}+2\right)}< 0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x>=9\\9\sqrt{x}-27-4\sqrt{x}-8< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=9\\5\sqrt{x}< 35\end{matrix}\right.\)
=>9<=x<49
