2ˣ+2⁽¹⁻ˣ⁾<3
2ˣ+2*2⁻ˣ<3
2ˣ+2/2ˣ<3 |×2ˣ
2²ˣ+2<3*2ˣ
2²ˣ-3*2ˣ+2<0
Пусть 2ˣ=t ⇒
t²-3t+2<0
t²-3t+2=0 D=1
t₁=2ˣ=2 x₁=1
t₂=2ˣ=1 x₂=0
(2ˣ-2)*(2ˣ-1)<0
-∞___+___0___-___1___+___+∞
ответ: x∈(0;1).
2ˣ+2⁽¹⁻ˣ⁾<3
2ˣ+2*2⁻ˣ<3
2ˣ+2/2ˣ<3 |×2ˣ
2²ˣ+2<3*2ˣ
2²ˣ-3*2ˣ+2<0
Пусть 2ˣ=t ⇒
t²-3t+2<0
t²-3t+2=0 D=1
t₁=2ˣ=2 x₁=1
t₂=2ˣ=1 x₂=0
(2ˣ-2)*(2ˣ-1)<0
-∞___+___0___-___1___+___+∞
ответ: x∈(0;1).