\(\frac{1}{3}=\frac{1.\sqrt{a}}{3.\sqrt{a}}=\frac{\sqrt{a}}{3\sqrt{a}}\\ \Rightarrow\frac{\sqrt{a}-2}{3\sqrt{a}}< \frac{\sqrt{a}}{3\sqrt{a}}\\ \Leftrightarrow\frac{\sqrt{a}-2}{3\sqrt{a}}< \frac{1}{3}\)
\(\frac{\sqrt{a}-2}{3\sqrt{a}}=\frac{1}{3}-\frac{2}{3\sqrt{a}}\)
Mà \(\sqrt{a}>0\Rightarrow\frac{2}{3\sqrt{a}}>0\Rightarrow\frac{1}{3}-\frac{2}{3\sqrt{a}}< \frac{1}{3}\)
Ta có: \(1-\frac{2}{\sqrt{a}}< 1,\forall a>0\)
\(\Leftrightarrow\frac{\sqrt{a}-2}{\sqrt{a}}< 1\)
\(\Leftrightarrow\frac{\sqrt{a}-2}{3\sqrt{a}}< \frac{1}{3}\)
