Đáp án:
\(\begin{array}{l}
a)A = a - \sqrt a + 2\\
b)Min = \dfrac{7}{4}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)A = \dfrac{{\sqrt a \left( {\sqrt a + 1} \right)\left( {a - \sqrt a + 1} \right)}}{{a - \sqrt a + 1}} - \dfrac{{\sqrt a \left( {2\sqrt a + 1} \right)}}{{\sqrt a }} + 3\\
= \sqrt a \left( {\sqrt a + 1} \right) - 2\sqrt a - 1 + 3\\
= a - \sqrt a + 2\\
b)A = a - \sqrt a + 2\\
= a - 2\sqrt a .\dfrac{1}{2} + \dfrac{1}{4} + \dfrac{7}{4}\\
= {\left( {\sqrt a - \dfrac{1}{2}} \right)^2} + \dfrac{7}{4}\\
Do:{\left( {\sqrt a - \dfrac{1}{2}} \right)^2} \ge 0\forall a\\
\to {\left( {\sqrt a - \dfrac{1}{2}} \right)^2} + \dfrac{7}{4} \ge \dfrac{7}{4}\\
\to Min = \dfrac{7}{4}\\
\Leftrightarrow \sqrt a - \dfrac{1}{2} = 0\\
\to a = \dfrac{1}{4}
\end{array}\)
