Решите неравенство: 14x/(x+6)-6*корень из (14x/(x+6))-7>=0.

\[\frac{14x}{x + 6} - 6\sqrt{\frac{14x}{x + 6}} - 7 \geq 0;\ \ \ \ \]

\[t = \sqrt{\frac{14x}{x + 6}}\]

\[t^{2} - 6t - 7 \geq 0\]

\[(t - 7)(t + 1) \geq 0\]

\[t \leq - 1;\ \ \ t \geq 7\]

\[1)\ \sqrt{\frac{14x}{x + 6}} \leq - 1;\ \ \ \ \ \]

\[\sqrt{\frac{14x}{x + 6}} \geq 0 \Longrightarrow нет\ решения.\]

\[2)\ \sqrt{\frac{14x}{x + 6}} \geq 7\]

\[\frac{14x}{x + 6} \geq 49\]

\[\frac{14x - 49 \cdot (x + 6)}{x + 6} \geq 0\]

\[\frac{14x - 49x - 294}{x + 6} \geq 0\]

\[\frac{- 35x - 294}{x + 6} \geq 0\]

\[\frac{- 7 \cdot (5x + 42)}{x + 6} \geq 0\]

\[\frac{5x + 42}{x + 6} \leq 0\]

\[\frac{5 \cdot (x + 8,4)}{x + 6} \leq 0\]

\[Ответ:\lbrack - 8,4;6).\]