Question

Решите неравенство: корень 2^х-2/2^х-4<1

Answer 1

$sqrt{frac{2^{x}-2}{2^{x}-4} } textless 1; ;; ; ; ; ODZ:; 2^{x}-4ne 0; ;; 2^{x}ne 2^2; ;; xne 2$

$frac{2^{x}-2}{2^{x}-4} geq 0\\+++[2]---(4)+++\\ left { {{2^{x} textgreater 4} atop {2^{x} leq 2}} right. left { {{2^{x} textgreater 2^2} atop {x leq 1}} right. left { {{x textgreater 2} atop {x leq 1}} right. ;xin (-infty ,1]cup (2,+infty )$

$frac{2^{x}-2}{2^{x}-4} -1 textless 0\\ frac{2^{x}-2-2^{x}+4}{2^{x}-4} textless 0\\ frac{2}{2^{x}-4} textless 0\\Tak; kak; ; 2 textgreater 0; ,; to; ; 2^{x}-4 textless 0\\2^{x} textless 2^2\\x textless 2\\Otvet:; ; xin (-infty ,1]; .$