Question

(8^x + 2^x)/(4^x -2) =5

Answer 1

(8^х+2^х)/(4^х-2)=5
ОДЗ х€(-бес.;+бес );4^х-2#0;х#1/2
(2^(3х)+2^х)/(2^(2х)-2)=5
2^х=t>0
t^3+t=5(t^2-2)
t^3-5t^2+t+10=0
(t-2)(t^2-3t-5)=0
1)t-2=0;t=2
2)t^2-3t-5=0
D=9+20=29
t1=(3+√29)/2
t2=(3-√29)/2<0 не подходит
2^х=2;х=1
2^х=(3+√29)/2
х=log(2)((3+√29)/2)