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vanek20003
@vanek20003
August 2022
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Решите неравенство. СРОЧНО!!!!!!!!!
0.4^x-2.5^(x+1)>1.5
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sangers1959
Verified answer
0,4ˣ-2,5ˣ⁺¹>1,5
(2/5)ˣ-(5/2)ˣ⁺¹>3/2
1/(5/2)ˣ-(5/2)*(5/2)ˣ>3/2
(5/2)ˣ=t>0
1/t-(5/2)*t>3/2
(5/2)*t²+(3/2)*t-1<0 |×2
5t²+3t-2<0
5t²+3t-2=0 D=49
t₁=-1
t₂=2/5
(t+1)(t-2/5)<0
((5/2)ˣ+1)((5/2)ˣ-(2/5))<0
(5/2)ˣ+1>0 ⇒
(5/2)ˣ-2/5<0
(5/2)ˣ<2/5
(5/2)ˣ<(5/2)⁻¹
x<-1.
Ответ: х∈(-∞;-1).
6 votes
Thanks 3
vanek20003
Спасибо большое!
sangers1959
Удачи!
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Answers & Comments
Verified answer
0,4ˣ-2,5ˣ⁺¹>1,5(2/5)ˣ-(5/2)ˣ⁺¹>3/2
1/(5/2)ˣ-(5/2)*(5/2)ˣ>3/2
(5/2)ˣ=t>0
1/t-(5/2)*t>3/2
(5/2)*t²+(3/2)*t-1<0 |×2
5t²+3t-2<0
5t²+3t-2=0 D=49
t₁=-1
t₂=2/5
(t+1)(t-2/5)<0
((5/2)ˣ+1)((5/2)ˣ-(2/5))<0
(5/2)ˣ+1>0 ⇒
(5/2)ˣ-2/5<0
(5/2)ˣ<2/5
(5/2)ˣ<(5/2)⁻¹
x<-1.
Ответ: х∈(-∞;-1).