Question

Решите неравенство 2^x+ 3 *2^-x<=4

Answer 1

$2^{x}+3cdot 2^{-x} leq 4\\2^{x}+frac{3}{2^{x}}-4 leq 0\\t=2^{x} textgreater 0; ,quad t+frac{3}{t}-4 leq 0\\ frac{t^2-4t+3}{t} leq 0; ,\\ frac{(t-1)(t-3)}{t} leq 0qquad ; ; ---(0)+++[, 1, ]---[, 3, ]+++\\tin (-infty ,0)cup [, 1,3, ]qquad Rightarrow; ; ; left [ {{t textless 0} atop {1 leq t leq 3}} right. \\2^{x} textless 0; ; net; ; reshenij; ,; ; tak; kak; 2^{x} textgreater 0\\1 leq 2^{x} leq 3; ; ; Rightarrow ; ; ; 2^0leq 2^{x}leq 2^{log_23}\\0 leq x leq log_23$

$xin [, 0, ,; log_23, ]$