(4^x - 2^(x+1) + 8) / 2^(1-x) < 8^x

Question

(4^x - 2^(x+1) + 8) / 2^(1-x) < 8^x

Answer 1

(2^2x-2*2^x+8)/(2/2^x)<2^3x<br>2^x=a
(a²-2a+8)*a/2(a²-2a+8)*a/2-a³<0<br>(a³-2a²+8a-2a³)/2<0<br>(-a³-2a²+8a)/2<0<br>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)---------
-4a>2⇒2^x>2⇒x>1
x∈(1;∞)