Решите неравенство (корень из x+x)(x-5корень из x+6)<=0.

\[\left( \sqrt{x} + x \right)\left( x - 5\sqrt{x} + 6 \right) \leq 0\ \ \ \ \ \ \ \ \ \]

\[Пусть\ \ t = \sqrt{x};\ \ \ t \geq 0:\]

\[\left( t + t^{2} \right)\left( t^{2} - 5t + 6 \right) \leq 0\]

\[t^{2} - 5t + 6 = 0\]

\[t_{1} = 3;\ \ \ t_{2} = 2\]

\[t(t + 1)(t - 3)(t - 2) \leq 0\]

\[- 1 \leq t \leq 0 \Longrightarrow t = 0\]

\[2 \leq t \leq 3\]

\[\sqrt{x} = 0 \Longrightarrow x = 0\]

\[2 \leq \sqrt{x} \leq 3 \Longrightarrow 4 \leq x \leq 9.\]

\[Ответ:\ \ \left\{ 0 \right\} \cup \lbrack 4;9\rbrack.\]