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