Question

помогите решит неравенство:
(log(2)^2x - 3log(2)x)^2 + 66log(2)x + 72 < 22 log(2)^2x

Answer 1

(log²(2)x-3log(2)x)²-22(log²(2)x-3log(2)x)+72<0
log²(2)x-3log(2)x=a
a²-22a+72<0
a1+a2=22 U a1*a2=72
a1=4 U a2=18
4<a<18
{log²(2)x-3log(2)x>4  (1)
{log²(2)x-3log(2)x<18  (2)
(1)
log(2)x=n
n²-3n-4>0
n1+n2=3 U n1*n2=-4
n1=-1 U n2=4
n<-1 U n>4
(2)
n²-3n<18
n²-3n-18<0
n1+n2=3 U n1*n2=-18
n1=-3 U n2=6
-3<n<6
-3<n<-1⇒-3<log(2)x<-1⇒1/8<x<1/2
4<n<6⇒4<log(2)x<6⇒16<x<64
Ответ x∈(1/8;1/2) U (16;64)