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treyvz888
@treyvz888
September 2021
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Решите неравенство методом интервалов. 1) 2^x-1/2x-1>0 2) (x^2-4)[tex] log_{ \frac{1}{2} } [/tex]x[tex] \leq [/tex]0
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oganesbagoyan
Verified answer
1)
2^x -1/(2x -1)> 0
⇔2^x >1/(2x -1).наглядно графическое решение .
**********************************
2)
(x² -4)*Loq_1/2 x ≤ 0 ;
x =1 и x=2 решении неравенства .
(x+2)(x-2)* Loq_1/2 x < 0 ;
а)
{ (x+2)(x-2) < 0 ; Loq_1/2 x > 0 .
{ -2< x <2 ; 0<x< 1. ⇒
x∈(0;1)
.
б)
{ (x+2)(x-2) > 0 ; Loq_1/2 x < 0 .
{ [ x∈(-∞; -2) U (2 ;∞) ; x>1 .
x∈(2;
∞
)
.
ответ :
x∈ (0; 1] U [2;∞) .
====================
или методом интервалов.
1 votes
Thanks 1
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Answers & Comments
Verified answer
1) 2^x -1/(2x -1)> 0 ⇔2^x >1/(2x -1).наглядно графическое решение .**********************************
2) (x² -4)*Loq_1/2 x ≤ 0 ;
x =1 и x=2 решении неравенства .
(x+2)(x-2)* Loq_1/2 x < 0 ;
а) { (x+2)(x-2) < 0 ; Loq_1/2 x > 0 .
{ -2< x <2 ; 0<x< 1. ⇒x∈(0;1).
б) { (x+2)(x-2) > 0 ; Loq_1/2 x < 0 .
{ [ x∈(-∞; -2) U (2 ;∞) ; x>1 . x∈(2;∞).
ответ : x∈ (0; 1] U [2;∞) .
====================
или методом интервалов.