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danafarn2013
@danafarn2013
September 2021
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Решите 21 и 24 примеры, подробное решение пожалуйста ;)
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oganesbagoyan
Verified answer
21)
(0,1)^(2x+1)/(1-x) >10³ ;
10^(2x+1)/(x-1) >10³
;
(2x+1)/(x-1) > 3 ;
(2x+1)/(x-1) - 3 >0 ;
(2x+1 -3x+3)/(x-1) >0 ;
(x-4)/(x-1) <0;
(x-1)(x-4) <0 ;
ответ :x∈(1;4).
-------------------
24) 5^(2x+1) >5^x +4 ;
5*(5^x)² -5^x -4 >0 ; * * * t =5^x * * *
5t² -t -4>0 ;
5(5^x+4/5)(5^x -1) >0 ;
5(5^x+4/5) > 0 ⇒ 5^x -1>0 ⇔5^x >5^0;
x ∈(0 ;∞)
ответ: x ∈(0 ;∞) .
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Answers & Comments
Verified answer
21)(0,1)^(2x+1)/(1-x) >10³ ;10^(2x+1)/(x-1) >10³ ;
(2x+1)/(x-1) > 3 ;
(2x+1)/(x-1) - 3 >0 ;
(2x+1 -3x+3)/(x-1) >0 ;
(x-4)/(x-1) <0;
(x-1)(x-4) <0 ;
ответ :x∈(1;4).
-------------------
24) 5^(2x+1) >5^x +4 ;
5*(5^x)² -5^x -4 >0 ; * * * t =5^x * * *
5t² -t -4>0 ;
5(5^x+4/5)(5^x -1) >0 ;
5(5^x+4/5) > 0 ⇒ 5^x -1>0 ⇔5^x >5^0;
x ∈(0 ;∞)
ответ: x ∈(0 ;∞) .