Question

sa se rezolve in R ecuatia
$5^{x}- 3^{x+1}\ \textgreater \ 2(5^{x-1}- 3^{x+2})$

Answer 1

[tex]5^x-2\cdot5^{x-1}\ \textgreater \ 3^{x+1}-2\cdot3^{x+2}\Leftrightarrow\\5^{x-1}(5-2)\ \textgreater \ 3^{x+1}(1-2\cdot3)\Leftrightarrow\\ \frac{5^{x-1}}{3^{x+1}}\ \textgreater \ \frac{-5}{3}[/tex]
Ultima inegalitate are loc pentru orice x∈R.
Deci S=R