Question

Помогите решить неравенства, какие сможете, но если вдруг все, то спасибо большое

Answer 1

26.

$\frac{-54}{x^{2} -49}\leq 0 <=>\frac{54}{x^{2} -49}\geq 0<=>\left \{ {{54>0} \atop {x^2-49>0}} \right.$

$x^{2} -7^2>0$

$(x-7)(x+7)>0$

//////////////////////////-7___________________7/////////////////////////////////////

Ответ:  $x<-7;$     $x>7.$

27.

$\frac{x^2+9}{4x^{2} -1}<0$

$\frac{x^2+9}{4x^{2} -1}<0 <=>\left \{ {{x^{2} +9>0} \atop {4x^2-1<0}} \right.<=>\left \{ {{-\infty<x<+\infty} \atop {(2x-1)(2x+1)<0}} \right.$

$(x-0,5)(x+0,5)<0$

_______________-0,5//////////////////////0,5__________________

Ответ:   $-0,5<x<0,5$

28.

$\frac{10}{1-100x^{2} } <0$

$\frac{10}{1-100x^{2} } <0<=>\left \{ {{10>0} \atop {1-100x^{2} <0}} \right. <=>\left \{ {{10>0} \atop {100x^{2}-1 >0}} \right. <=>\left \{ {{10>0} \atop {x^{2}-(0,1)^2 >0}} \right. <=>$

$<=>\left \{ {{10>0} \atop {(x-0,1)(x+0,1) >0}} \right.$

                 $(x-0,1)(x+0,1) >0$

/////////////////////-0,1__________0,1//////////////////////////////

Ответ:   $x<-0,1;$    $x>0,1.$