Question

решите неравенство методом интервалов (x2-25)(x-2)(x-4)>0

Answer 1

$(x^{2} - 25)(x - 2)(x-4) >0$

$\left \{ {{\bigg{ \ (x^{2} - 25)(x - 2) > 0}} \atop {\bigg{x - 4 > 0 \ \ \ \ \ \ \ \ \ \ \ \ }}} \right.$

$\left \{ {{\bigg{ \ (x^{2} - 25)(x - 2) < 0}} \atop {\bigg{x - 4 < 0 \ \ \ \ \ \ \ \ \ \ \ }}} \right.$

$\left \{ {{\bigg{ x \in (-5; 2) \cup (5; +\infty)}} \atop {\bigg{x > 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }}} \right.$

$\left \{ {{\bigg{ x \in (-\infty; -5) \cup (2; 5)}} \atop {\bigg{x < 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }}} \right.$

$x \in (5; +\infty)$

$x \in (-\infty; -5) \cup (2; 4)$

Ответ: $x \in (-\infty; -5) \cup(2;4) \cup (5; +\infty)$