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Решите неравенство:
[tex]3*9^{x} -2*15^{x} -5^{2x+1} \ \textgreater \ 0[/tex]
Решите неравенство:
[tex]3*9^{x} -2*15^{x} -5^{2x+1} \ \textgreater \ 0[/tex]
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3*9ˣ-2*15ˣ-5²ˣ⁺¹>03*3²ˣ-2*3ˣ*5ˣ-5*5²ˣ>0 |÷3²ˣ
3-2*(5ˣ/3ˣ)-5*(5²ˣ/3²ˣ)>0
3-2*(5/3)ˣ-5*(5/3)²ˣ>0
Пусть (5/3)ˣ=t>0 ⇒
3-2t-5t²>0 |÷(-1)
5t²+2t-3<0
5t²+2t-3=0 D=64
t₁=3/5
t₂=-1 ⇒
(t-(3/5))*(t+1)<0
((5/3)ˣ-(3/5))*((5/3)ˣ+1)<0
(5/3)ˣ+1>0 ⇒
(5/3)ˣ-(3/5)<0
(5/3)ˣ<3/5
(5/3)ˣ<(5/3)⁻¹
x<-1.
Ответ: x∈(-∞;-1).