Question

2^х +2^-х+1 -3 <0
Срочно!

Answer 1

$2^{x}+2^{-x+1}-3 textless 0\\2^{x}+2^{-x}cdot 2^1-3 textless 0\\2^{x}+frac{2}{2^{x}}-3 textless 0\\t=2^{x} textgreater 0; ,; ; ; t+frac{2}{t}-3 textless 0\\ frac{t^2-3t+2}{t} textless 0; ; to ; ; frac{(t-1)(t-2)}{t} textless 0\\---(0)+++(1)---(2)+++\\tin (-infty ,1)cup (1,2)\\t textgreater 0; ; Rightarrow quad tin (1,2); ; Rightarrow quad 1 textless 2^{x} textless 2quad Rightarrow \\2^0 textless 2^{x} textless 2^1\\0 textless x textless 1\\underline {xin (0,1)}\\\P.S.quad t^2-3t+2=0; ; Rightarrow quad t_1=1,; t_2=2; ; (teorema; Vieta); ; to \\t^2-3t+2=(t-1)(t-2)$