решите пожалуйста уравнения. Created by meme9. algebra-ru

9.26а) Log_2 (x+2) +Log_2 (x-3) =Log_2 (x² -5x+6) ;{ x+2 >0 ; x -3>0. ⇒x >3Если x >3,то Log_2 (x+2)+Log_2 (x-3) =Log_2 (x+2) *(x-3)=Log_2 x² -5x+6)ответ: любое число больше 3 , иначе x∈(3;∞) .---в) Lg(x² -5x+6) +Lg(5x -x² -4) =Lg ( (x² -5x+6) (5x -x² -4) );{x² -5x+6 >0 ; 5x -x² -4 >0.⇔{(x-2)(x-3) >0; (x- 1)(x-4) <0 .⇔{x∈(-∞ ;2)U (3 ;∞); x∈(1 ;4).⇔x∈(1;2) U(3;4).ответ: x∈(1;2) U(3;4).----------9.27а) Loq_x (2x² -2x -3) =2 ;ОДЗ : { 2x² -2x -3 >0 ;x >0; x ≠1.2x² -2x -3 = x² ;x² -2x -3 =0 ;[ x = -1 ; x=3. x = -1 ∉ ОДЗ.ответ: 3.---в) Log_x (x+2) =2 ;ОДЗ : { x >0; x ≠1; x+2.В ОДЗ x+2=x² ;x² - x -2 =0 ;[x = -1 ; x =2 .x = -1 ∉ ОДЗ .ответ: 2 .Новые вопросы в АлгебраДОПОМОЖІТЬ БУДЬ ЛАСКАТри різних корені рівняння x³ + (a² - 14a)x² + 39ax - 27 = 0 утворюють геометричну прогресію. Знайти: 1) значення параметра a; 2) суму цих членів.y = x⁴ + 3cosx Знайти похідну функцііСкільки коренів має утворення 9+×=36 100балів пж Потрібно будь-яких 5 завдань з першого варіантуНа менше плече сили діє сила 400 Н, на більше 20 Н. Довжина більшого плеча 10 см. Визначте довжину меншого плеча СРОЧНО!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!…!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Срочнооо 80 балів!!!!!Поможіть будь ласкаСума двох додатних чисел дорівнює 2•N +10. Які мають бути числа, щоб сума квадратів цих чисел була найменшийбудь ласка, допоможіть!ПредыдущийСледующийВместе мы знаем большеЭтот сайт использует cookies Политика Cookies . 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June 2022 1 14 Report

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Answers & Comments

oganesbagoyan

Verified answer

9.26
а) Log_2 (x+2) +Log_2 (x-3) =Log_2 (x² -5x+6) ;
{ x+2 >0 ; x -3>0. ⇒x >3
Если x >3,то Log_2 (x+2)+Log_2 (x-3) =Log_2 (x+2) *(x-3)=Log_2 x² -5x+6)
ответ: любое число больше 3 , иначе x∈(3;∞) .
---
в) Lg(x² -5x+6) +Lg(5x -x² -4) =Lg ( (x² -5x+6) (5x -x² -4) );
{x² -5x+6 >0 ; 5x -x² -4 >0.⇔{(x-2)(x-3) >0; (x- 1)(x-4) <0 .⇔
{x∈(-∞ ;2)U (3 ;∞); x∈(1 ;4).⇔x∈(1;2) U(3;4).
ответ: x∈(1;2) U(3;4).
----------
9.27
а) Loq_x (2x² -2x -3) =2 ;
ОДЗ : { 2x² -2x -3 >0 ;x >0; x ≠1.
2x² -2x -3 = x² ;
x² -2x -3 =0 ;
[ x = -1 ; x=3.
x = -1 ∉ ОДЗ.
ответ: 3.
---
в) Log_x (x+2) =2 ;
ОДЗ : { x >0; x ≠1; x+2.
В ОДЗ x+2=x² ;
x² - x -2 =0 ;
[x = -1 ; x =2 .
x = -1 ∉ ОДЗ .

ответ: 2 .