Question

Answer 1

\(a,P=\dfrac{\sqrt{x}-\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}:\dfrac{x-1-x+4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}\\ P=\dfrac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}\cdot\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}{3}=\dfrac{\sqrt{x}-2}{3\sqrt{x}}\\ b,P=\dfrac{1}{4}\Leftrightarrow4\left(\sqrt{x}-2\right)=3\sqrt{x}\\ \Leftrightarrow\sqrt{x}=8\\ \Leftrightarrow x=64\\ c,P< 0\Leftrightarrow\dfrac{\sqrt{x}-2}{3\sqrt{x}}< 0\Leftrightarrow\sqrt{x}-2< 0\left(3\sqrt{x}>0\right)\\ \Leftrightarrow0< x< 4\)