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MichaIlov
@MichaIlov
August 2022
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Алгебра 11 класс,показательные неравенства
Решите с 18 по 21 пжлст
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sedinalana
Verified answer
18
5^x*(x²-25)=0
5^x>0 при любом х
x²-25=0
x²=25
x=-5 U x=5
19
2^2x+2^2^x-80≤0
2^x=a
a²+2a-80≤0
a1=a2=-2 U a18a2=-80
a1=-10 U a2=8
-10≤2^x≤8
x≤3
x∈(-∞;3]
20
2^2^(-2x)-7*2^(-x)-4<0
2^(-x)=a
2a²-7a-4<0
D=49+32=81
a1=(7-9)/4=-1/2 U a2=(7+9)/4=4
-1/2<2^(-x)<4
-x<2
x>-2
x∈(-2;∞)
21
ОДЗ
(x-√3)(x+√3)≥0
x∈(-∞;-√3] U [√3;∞)
9^(√(x²-3) -28/3*3^√(x²-3)+3<0
3^√(x²-3)
3a²-28a+9<0
D=784-108=676
a1=(28-26)/6=1/3
a2=(28+26)/6=9
1/3<3^√(x²-3)<9
-1<√(x²-3)<2
x²-3<4
x²-7<0
(x-√7)(x+√7)<0
-√7<x<√7
x∈(-√7;-√3] U [√3;√7)
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Answers & Comments
Verified answer
185^x*(x²-25)=0
5^x>0 при любом х
x²-25=0
x²=25
x=-5 U x=5
19
2^2x+2^2^x-80≤0
2^x=a
a²+2a-80≤0
a1=a2=-2 U a18a2=-80
a1=-10 U a2=8
-10≤2^x≤8
x≤3
x∈(-∞;3]
20
2^2^(-2x)-7*2^(-x)-4<0
2^(-x)=a
2a²-7a-4<0
D=49+32=81
a1=(7-9)/4=-1/2 U a2=(7+9)/4=4
-1/2<2^(-x)<4
-x<2
x>-2
x∈(-2;∞)
21
ОДЗ
(x-√3)(x+√3)≥0
x∈(-∞;-√3] U [√3;∞)
9^(√(x²-3) -28/3*3^√(x²-3)+3<0
3^√(x²-3)
3a²-28a+9<0
D=784-108=676
a1=(28-26)/6=1/3
a2=(28+26)/6=9
1/3<3^√(x²-3)<9
-1<√(x²-3)<2
x²-3<4
x²-7<0
(x-√7)(x+√7)<0
-√7<x<√7
x∈(-√7;-√3] U [√3;√7)