Question

Решить неравенство с логарифмом.
Даю 100 баллов.

Answer 1

$\displaystyle log_{\frac{1}{2} }(8+5x-x^2) < -3, x \in (\frac{5-\sqrt{57} }{2},\frac{5+\sqrt{57} }{2})\\ \\8+5x-x^2 > (\frac{1}{2})^-^3\\ \\8+5x-x^2 > 2^3\\ 8+5x-x^2 > 8\\ 5x-x^2 > 0\\x(5-x) > 0\\\\\left \{ {{x > 0} \atop {5-x > 0}} \right. \rightarrow\left \{ {{x > 0 \atop {x < 5}} \right. \rightarrow x \in (0,5)\\\\\left \{ {{x < 0} \atop {5-x < 0}} \right. \rightarrow \left \{ {{x < 0} \atop {x > 5}} \right. \rightarrow \oslash\\ \\x \in (0,5)$