![image](https://tex.z-dn.net/?f=4%5E%7Bx%7D%2B%5Cfrac%7B1%7D%7B4%5Ex%7D%3E2%5C%5C%0A4%5Ex%3Da%5C%5C%0Aa%2B%5Cfrac%7B1%7D%7Ba%7D%3E2%5C%5C%0Aa%5E2-2a%2B1%3E0%5C%5C%0A%28a-1%29%5E2%3E0+%0Aa+%5Cneq+0%5C%5C%0A4%5Ex%3E0%0A)
2\\
4^x=a\\
a+\frac{1}{a}>2\\
a^2-2a+1>0\\
(a-1)^2>0
a \neq 0\\
4^x>0
" alt="4^{x}+\frac{1}{4^x}>2\\
4^x=a\\
a+\frac{1}{a}>2\\
a^2-2a+1>0\\
(a-1)^2>0
a \neq 0\\
4^x>0
" align="absmiddle" class="latex-formula">
откуда для а получаем интервал
![(0;1) U (1;+oo)\\ (0;1) U (1;+oo)\\](https://tex.z-dn.net/?f=%280%3B1%29+U+%281%3B%2Boo%29%5C%5C)
, а для х получаем