Question

помогите решить неравенство пожалуйста

Answer 1

ОДЗ: x² - 2x - 8 > 0
         (x - 4)(x + 2)  > 0
        +                    -                         +
________₀_____________₀_____________
                 - 2                        4
x ∈ (- ∞ ; - 2)∪(4 , + ∞)

$log _{ \frac{1}{3} } ( x^{2} -2x-8)\ \textgreater \ - 3\\\\ x^{2} -2x-8\ \textless \ ( \frac{1}{3}) ^{-3}\\\\ x^{2} -2x-8\ \textless \ 27\\\\ x^{2} -2x-35\ \textless \ 0\\\\(x-7)(x+5)\ \textless \ 0$
          +                            -                          +
____________₀_____________₀____________
                         - 5                        7
x ∈ (- 5 ; 7)
C учётом ОДЗ окончательный ответ:
x ∈ ( - 5 ; - 2)∪(4 , 7)

Answer 2

{x²-2x-8>0⇒(x-4)(x+2)>0⇒x<-2 U x>4
{log(1/3)(x²-2x-8)>-3⇒x²-2x-8<27⇒x²-2x-35<0⇒(x-7)(x+5)<0⇒-5<x<7
           ///////////////////////////////////////////////////
--------(-5)--------(-2)----------(4)-----------(7)---------
///////////////////////////                 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
x∈(-5;-2) U (4;7)