Question

Решите неравенство. СРОЧНО!!!!!!!!!
0.4^x-2.5^(x+1)>1.5

Answer 1

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).