\(P=\frac{\sqrt{a}\left(a\sqrt{a}+1\right)}{a-\sqrt{a}+1}-\frac{\sqrt{a}\left(2\sqrt{a}+1\right)}{\sqrt{a}}+1\)
\(=\frac{\sqrt{a}\left(\sqrt{a}+1\right)\left(a-\sqrt{a}+1\right)}{a-\sqrt{a}+1}-\left(2\sqrt{a}+1\right)+1\)
\(=\sqrt{a}\left(\sqrt{a}+1\right)-2\sqrt{a}=a-\sqrt{a}\)
\(P=2\Rightarrow a-\sqrt{a}=2\Rightarrow a-\sqrt{a}-2=0\)
\(\Rightarrow\left(\sqrt{a}+1\right)\left(\sqrt{a}-2\right)=0\Rightarrow\sqrt{a}=2\Rightarrow a=4\)
\(P=a-\sqrt{a}=a-\sqrt{a}+\frac{1}{4}-\frac{1}{4}=\left(\sqrt{a}-\frac{1}{2}\right)^2-\frac{1}{4}\ge-\frac{1}{4}\)
\(\Rightarrow P_{min}=-\frac{1}{4}\) khi \(\sqrt{a}=\frac{1}{2}\Rightarrow a=\frac{1}{4}\)
