Question

.
$25 {}^{x} - 6 \times 5 {}^{x} + 5 > 0$
Помогите решить​

Answer 1

${25}^{x} - 6 \times {5}^{x} + 5 > 0 \\ { {(5}^{2}) }^{x} - 6 \times {5}^{x} + 5 > 0 \\ { ({5x}^{x}) }^{2} - 6 \times {5}^{x} + 5 > 0 \\ {t}^{2} - 6t + 5 > 0 \\ x∈( - 8;1)U(5; + \infty ) \\ {5}^{x} ∈( - \infty ; + 1)U(5; + \infty ) \\ {5}^{x} < 1 \\ {5}^{x} > 5 \\ x < 0 \\ x > 1 \\ x∈( - \infty ;0)U(1; + \infty )$

Answer 2

$25^{x}-6*5^{x}+5>0\\\\5^{x}=m \ , \ m>0\\\\m^{2}-6m+5>0\\\\ (m-1)(m-5) >0$

     +             -               +

______₀_______₀_______  m

            1               5

\\\\\\\\\\\\\               ///////////////

$1)m<1\\\\5^{x} <1\\\\5^{x}<5^{0}\\\\x<0\\\\2)m>5\\\\5^{x} >5\\\\x>1\\\\Otvet:\boxed{x\in(-\infty \ ; \ 0) \ \cup \ (1 \ ; \ +\infty)}$