Help me!!!! Решите пожалуйста неравенство log 1/3 (x^2-2x-8)+3>0. Created by katme14. algebra-ru

ОДЗ : x² - 2x - 8 > 0(x - 4)(x + 2) > 0 + - +_____________₀__________₀___________ - 2 4////////////////////////// ///////////////////////////x ∈ ( - ∞ , - 2) ∪ (4 ; + ∞) + - +______________₀_____________₀_____________ - 5 7 ////////////////////////////x ∈ (- 5 , 7)С учётом ОДЗ окончательный ответ :x ∈ (- 5 ; - 2) ∪ (4 , 7)

3 (x^2-2x-8)+3>0...

Хуqожнuк

ОДЗ :

x² - 2x - 8 > 0

(x - 4)(x + 2) > 0

+ - +

_____________₀__________₀___________

- 2 4

////////////////////////// ///////////////////////////

x ∈ ( - ∞ , - 2) ∪ (4 ; + ∞)

$log_{\frac{1}{3} }(x^{2}-2x-8)+3>0\\\\log_{\frac{1}{3} }(x^{2}-2x-8)>-3\\\\x^{2}-2x-8$

+ - +

______________₀_____________₀_____________

- 5 7

////////////////////////////

x ∈ (- 5 , 7)

С учётом ОДЗ окончательный ответ :

x ∈ (- 5 ; - 2) ∪ (4 , 7)

0 votes Thanks 1

Universalka

Verified answer

ОДЗ:

$x^2-2x-8>0\\ \\ \sqrt{D}=\sqrt{4+8*4}=\sqrt{36}=6\\ \\ x_1=\frac{2-6}{2}=-2\\ \\ x_2=\frac{2+6}{2}=4\\ \\ \left \{ {{x4}} \right.$

____________________________________

$log_\frac{1}{3} (x^2-2x-8)+3>0\\ \\ -log_3(x^2-2x-8)+log_327>0\\ \\ log_3(x^2-2x-8)$

____________________________________

Объединяем ОДЗ и решение неравенства, получаем

x ∈ (-5; -2) ∪ (4; 7)

____________________________________

Ответ: (-5; -2) ∪ (4; 7)

0 votes Thanks 1

Answers & Comments

Verified answer

help me srochno 4 i 5 reshite pozhalujsta

srochno pomogite nuzhno podobrat takie chisla chtoby sistema byla verna

pomogite srochno napishite programmu kotoraya v posledovatelnosti naturalnyh

heip me rasstavte v hronologicheskom poryadke poyavleniya v istorii lokalnye ci

srochno pomogite pozhalujta ukazhite cel upravleniya upravlyayushij obekt u

pomogite srochno tri rezistora soprotivleniyami r13 om r26 om i r39 om soe

srochno heelp me

pomogite pozhalujsta nuzhno sopostavit funkcii shkoly s vidom funkcii funk

srochno pomogite pozhalujsta 2x 2sinx 2xsinx

heeelp me srochno zadanie 13 pod bukvoj b

рекомендуемые вопросы

Helpful Links

Helpful Social