\(P=\dfrac{a^2+\sqrt{a}}{a-\sqrt{a}+1}-\dfrac{2a+\sqrt{a}}{\sqrt{a}}+1\) (Đk:\(a>0\))
\(=\dfrac{\sqrt{a}\left(a\sqrt{a}+1\right)}{a-\sqrt{a}+1}-\dfrac{\sqrt{a}\left(2\sqrt{a}+1\right)}{\sqrt{a}}+1\)
\(=\sqrt{a}\left(\sqrt{a}+1\right)-2\sqrt{a}-1+1\)
\(=a-\sqrt{a}\)
b) \(P=2\Leftrightarrow a-\sqrt{a}=2\Leftrightarrow a-\sqrt{a}-2=0\)\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{a}=2\\\sqrt{a}=-1\left(vn\right)\end{matrix}\right.\)\(\Rightarrow a=4\) (tm)
Vậy a=4 thì P=2
c) \(P=a-\sqrt{a}=\left(\sqrt{a}-\dfrac{1}{2}\right)^2-\dfrac{1}{4}\ge-\dfrac{1}{4}\)
Dấu "=" xảy ra khi \(\sqrt{a}=\dfrac{1}{2}\Leftrightarrow a=\dfrac{1}{4}\)
Vậy \(P_{min}=-\dfrac{1}{4}\)
