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litanalove
@litanalove
July 2022
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(4^x - 2^(x+1) + 8) / 2^(1-x) < 8^x
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sedinalana
Verified answer
(2^2x-2*2^x+8)/(2/2^x)<2^3x
2^x=a
(a²-2a+8)*a/2<a³
(a²-2a+8)*a/2-a³<0
(a³-2a²+8a-2a³)/2<0
(-a³-2a²+8a)/2<0
a(a²+2a-8)/2>0
a=0
a²+2a-8=0
a1+a2=-2 U a1*a2=-8⇒a1=-4 U a2=2
_ + _ +
--------------(-4)---------(0)----------(2)---------
-4<a<0⇒-4<2^x<0 нет решения
a>2⇒2^x>2⇒x>1
x∈(1;∞)
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Answers & Comments
Verified answer
(2^2x-2*2^x+8)/(2/2^x)<2^3x2^x=a
(a²-2a+8)*a/2<a³
(a²-2a+8)*a/2-a³<0
(a³-2a²+8a-2a³)/2<0
(-a³-2a²+8a)/2<0
a(a²+2a-8)/2>0
a=0
a²+2a-8=0
a1+a2=-2 U a1*a2=-8⇒a1=-4 U a2=2
_ + _ +
--------------(-4)---------(0)----------(2)---------
-4<a<0⇒-4<2^x<0 нет решения
a>2⇒2^x>2⇒x>1
x∈(1;∞)