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Baohas
@Baohas
March 2022
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Решить уравнение: 3^x+15*3^-x<8
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sangers1959
Verified answer
3ˣ+15*3⁻ˣ<8
3ˣ+15/3ˣ-8<0
3²ˣ-8*3ˣ+15=0
3ˣ=t>0
t²-8t+15<0
t²-8t+15=0 D=4
t₁=3 3ˣ=3¹ x₁=1
t₂=5 3ˣ=5 x₂=log₃5
(t-1)(t-5)<0
-∞______+______3______-_______5______+______+∞
t∈(3;5) ⇒
x∈(1;log₃5).
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Answers & Comments
Verified answer
3ˣ+15*3⁻ˣ<83ˣ+15/3ˣ-8<0
3²ˣ-8*3ˣ+15=0
3ˣ=t>0
t²-8t+15<0
t²-8t+15=0 D=4
t₁=3 3ˣ=3¹ x₁=1
t₂=5 3ˣ=5 x₂=log₃5
(t-1)(t-5)<0
-∞______+______3______-_______5______+______+∞
t∈(3;5) ⇒
x∈(1;log₃5).