Question

(1/4)^x-4(1/2)^x>-4

Помогите пожалуйста

Answer 1

$\bigg(\frac{\big1}{\big4}\bigg)^x-4*\bigg(\frac{\big1}{\big2}\bigg)^x>-4\\\\\bigg(\frac{\big1}{\big4}\bigg)^x-4*\bigg(\frac{\big1}{\big2}\bigg)^x+4>0\\\\\Bigg(\:\bigg(\frac{\big1}{\big2}\bigg)^{x}\Bigg)^2-2*2*\bigg(\frac{\big1}{\big2}\bigg)^{x}+2^2>0\\\\Formyla\::\\\\\boxed{\:\:a^2-2*a*b+b^2=\Big(a-b\Big)^2\:\:}$

$\Bigg(\bigg(\frac{\big1}{\big2}\bigg)^x-2\Bigg)^2>0\\\\No\:\:\:\:\Bigg(\bigg(\frac{\big1}{\big2}\bigg)^x-2\Bigg)^2\geq0\:\:,\:\:\:tak\:\:\:kak\:\:\:\:Q^2\geq0\\\\\\Znahit\:,\:\:\:\bigg(\frac{\big1}{\big2}\bigg)^x-2\neq0\\\\\bigg(\frac{\big1}{\big2}\bigg)^x\neq2\:\:\:\Leftrightarrow\:\:\:2^{-x}\neq2^1\:\:\:\Leftrightarrow\:\:\:-x\neq1\:\:\:\Leftrightarrow\:\:\:x\neq-1\\\\\\\boxed{\:\:x\:\:\in\:\:\Big(-\infty\:;-1\:\Big)\:\:\cup\:\:\Big(-1\:\:;+\infty\:\Big)\:\:}$