Question

Помогите решить неравенство 11 класс
$2 ^{2x+1} -5*2^{x} +2 geq 0$

Answer 1

$2^{2x+1} -5cdot2^{x} +2 geq 0, \ 2cdot2^{2x}-5cdot2^{x} +2 geq 0, \ 2^{x}=t, t>0, \ 2t^2-5t+2 geq 0, \ 2t^2-5t+2 = 0, \ D=9>0, \ t_1=frac{1}{2}, t_2=2, \ a=2>0, \ left [ {{t leq frac{1}{2},} atop {t geq2;}} right. \ left [ {{2^{x}leq frac{1}{2},} atop {2^{x}geq2;}} right. left [ {{2^{x}leq2^{-1},} atop {2^{x}geq2^1;}} right. left [ {{x leq -1,} atop {x geq 1;}} right. \ xin(-infty;-1]cup[1;+infty).$