Đáp án:
\(0 < x < 36;x \ne 9\)
Giải thích các bước giải:
\(\begin{array}{l}
M = \dfrac{{2\sqrt x \left( {\sqrt x - 3} \right) + \left( {\sqrt x + 1} \right)\left( {\sqrt x + 3} \right) + 11\sqrt x - 3}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}}\\
= \dfrac{{2x - 6\sqrt x + x + 4\sqrt x + 3 + 11\sqrt x - 3}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}}\\
= \dfrac{{3x + 9\sqrt x }}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}}\\
= \dfrac{{3\sqrt x }}{{\sqrt x - 3}}\\
d)\dfrac{1}{M} < \dfrac{1}{6}\\
\to \dfrac{{\sqrt x - 3}}{{3\sqrt x }} < \dfrac{1}{6}\\
\to \dfrac{{2\sqrt x - 6 - \sqrt x }}{{6\sqrt x }} < 0\\
\to \dfrac{{\sqrt x - 6}}{{6\sqrt x }} < 0\\
\to \sqrt x - 6 < 0\left( {do:\sqrt x > 0\forall x > 0} \right)\\
\to 0 < x < 36;x \ne 9
\end{array}\)
