\(\begin{array}{l} a.B = \left[ {\dfrac{{\sqrt x + 1 + x}}{{\sqrt x \left( {\sqrt x + 1} \right)}}} \right]:\dfrac{{\sqrt x }}{{\sqrt x \left( {\sqrt x + 1} \right)}}\\ = \dfrac{{x + \sqrt x + 1}}{{\sqrt x \left( {\sqrt x + 1} \right)}}.\dfrac{{\sqrt x \left( {\sqrt x + 1} \right)}}{{\sqrt x }}\\ = \dfrac{{x + \sqrt x + 1}}{{\sqrt x }} = \sqrt x + 1 + \dfrac{1}{{\sqrt x }}\\ b.B = \sqrt x + 1 + \dfrac{1}{{\sqrt x }}\\ Do:x > 0\\ \to BDT:Cô - si:\sqrt x + \dfrac{1}{{\sqrt x }} \ge 2\sqrt {\sqrt x .\dfrac{1}{{\sqrt x }}} \\ \to \sqrt x + \dfrac{1}{{\sqrt x }} \ge 2\\ \to \sqrt x + \dfrac{1}{{\sqrt x }} + 1 \ge 3\\ \to Min = 3\\ \Leftrightarrow \sqrt x = \dfrac{1}{{\sqrt x }}\\ \Leftrightarrow x = 1 \end{array}\)
