Question

Решите неравенство ____

Answer 1

$\left[ \begin{gathered} \left\{ \begin{gathered} 3^x-9>0, \hfill \\ (3^{2x}-9*3^x)>(3^x-9)^2 \hfill \\ \end{gathered} \right. \hfill \\ \left\{ \begin{gathered} 3^x-9<0, \hfill \\ 3^{2x}-9*3^x\geq 0 \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} \right.$

1)

$\displaystyle \left \{ {{3^x>9} \atop {(3^x-9)(3^x-3^x+9)>0}} \right.\\\\\left \{ {{x>2} \atop {(3^x-9)*9>0}} \right.\\\\\left \{ {{x>2} \atop {x>2}} \right.$

x∈(2;+∞)

2)

$\displaystyle \left \{ {{x<2} \atop {3^x(3^x-9)\geq 0}} \right.\\\\\left \{ {{x<2} \atop {x\geq 2}} \right.$

нет решений

Ответ: (2;+∞)