Question

Решить уравнения а)2|ˣ|⁺² больше 1/8 b)2|ˣ|⁺² больше8 с) (1/2)|ˣ|⁺² больше 8 д) (1/2)|ˣ|⁺² больше 1/8

Answer 1

$2^{|x|+2|}\ \textgreater \ \frac{1}{8}\\\\2^{|x|+2|}\ \textgreater \ 2^{-3}\\|x|+2\ \textgreater \ -3\\|x|\ \textgreater \ -5$
x∈(-∞;+∞), т.к. |x|≥0 при любом значении х

$2^{|x|+2}\ \textgreater \ 8\\2^{|x|+2}\ \textgreater \ 2^3\\2\ \textgreater \ 1\\|x|+2\ \textgreater \ 3\\|x|\ \textgreater \ 1$
x<-1 и x>1
x∈(-∞;-1)U(1;+∞)

$( \frac{1}{2})^{|x|+2}\ \textgreater \ 8\\( \frac{1}{2})^{|x|+2}\ \textgreater \ ( \frac{1}{2})^{-3}\\0\ \textless \ \frac{1}{2}\ \textless \ 1\\|x|+2\ \textless \ -3\\|x|\ \textless \ -5$
x∈∅  (Решений нет)

$( \frac{1}{2})^{|x|+2}\ \textgreater \ \frac{1}{8}\\( \frac{1}{2})^{|x|+2}\ \textgreater \ ( \frac{1}{2})^3\\0\ \textless \ \frac{1}{2}\ \textless \ 1\\|x|+2\ \textless \ 3\\|x|\ \textless \ 1\\-1\ \textless \ x\ \textless \ 1\\x\in(-1;1)$