Question

Решите неравенство 4^x-6*2^x+8>0

Answer 1

$4^x-6*2^x+8\ \textgreater \ 0 \\ \\ 2^{2x} -6*2^x+8\ \textgreater \ 0 \\ \\ D=36-32=4 \\ \\ 2^x=(6-2)/2=2 \\ \\ 2^x=(6+2)/2=4=2^2 \\ \\ (2^x-2)(2^x-2^2)\ \textgreater \ 0 \\ \\ (x-1)(x-2)\ \textgreater \ 0 \\ \\ +++(1)---(2)+++ \\ \\ x\in(-oo;1)U(2;+oo)$