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korostylevkeks
@korostylevkeks
July 2022
1
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Помогите пожалуйста с 15 номером, ответ должен получится (-1; 0)U(0; 1/2]U(1; +бесконечность)!
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oganesbagoyan
Verified answer
Log_|x| (x-1)² ≤ 2 ;
ОДЗ: x ≠0 ,|x|≠ 1 ⇔x≠0 ;x ≠ -1 ; x≠1 .
x∈ (-∞ ;-1) U (-1;0) U (0;1) U (1;∞).
-------------
а)
x∈
(-1;0) U (0;1)
.
(x-1)² ≥ |x|² ;
x² -2x+1 ≥ x² ;
x ≤ 1/2. ⇒
x ∈( -1;0) U (0 ;1/2]
---
б)
x∈ (-∞ ;-1)
U
(1;∞)
.
(x-1)² ≤ |x|² ;
x² -2x+1 ≤ x² ⇒x ≥1/2 ⇒
x∈
(1;∞)
.
----
.
ответ :
x ∈( -1;0) U (0 ;1/2]
U
(1;∞)
.
1 votes
Thanks 1
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Answers & Comments
Verified answer
Log_|x| (x-1)² ≤ 2 ;ОДЗ: x ≠0 ,|x|≠ 1 ⇔x≠0 ;x ≠ -1 ; x≠1 .
x∈ (-∞ ;-1) U (-1;0) U (0;1) U (1;∞).
-------------
а) x∈ (-1;0) U (0;1) .
(x-1)² ≥ |x|² ;
x² -2x+1 ≥ x² ;
x ≤ 1/2. ⇒ x ∈( -1;0) U (0 ;1/2]
---
б) x∈ (-∞ ;-1) U(1;∞) .
(x-1)² ≤ |x|² ;
x² -2x+1 ≤ x² ⇒x ≥1/2 ⇒ x∈ (1;∞).
----
.
ответ : x ∈( -1;0) U (0 ;1/2] U (1;∞).