Question

2^х +2^-х+1 -3 <0 Срочно!

Answer 1

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