5^2x-6*5^x+5>0 ;
(5^x)² - 6*(5^x) +5 > 0; t =5^x >0;
* * * * * (5^x -1)(5^x -5) > 0 * * * * * *
t² -6 t +5 = 0;
t =3 ± √(3²-5) ;
t₁ =3 - 2 =1;
t₂ =3 + 2= 5.
(t -1)(t -5) > 0;
+ - +
-------------- 1 ----------5 -----------
[ t <1; t >5 .
[ 5^x <1 ; 5^x > 5.⇔ [ 5^x <5^0 ; 5^x > 5^1. ⇔ [ x <0 ; x>1.
ответ : x ∈ (-∞; 0) U (1 ;∞) .