Question

14
Решите, пожалуйста

Answer 1

$25^x-9*4^{x-1}*5^x+5*4^{2x-1} textgreater 0\\ 5^{2x}-frac{9}{4}*4^{x}*5^x+frac{5}{4}*4^{2x} textgreater 0 | * frac{1}{4^x*5^x}\\ frac{5^{2x}}{4^x*5^x}-frac{9}{4}+frac{5}{4}*frac{4^{2x}}{4^x*5^x} textgreater 0*frac{1}{4^x*5^x}\\ frac{5^{x}}{4^x}-frac{9}{4}+frac{5}{4}*frac{4^{x}}{5^x} textgreater 0\\ (frac{5}{4})^x-frac{9}{4}+frac{5}{4}*(frac{4}{5})^x textgreater 0\\ (frac{5}{4})^x=t textgreater 0\\ t-frac{9}{4}+frac{5}{4}*frac{1}{t} textgreater 0\\ frac{4t^2-9t+5}{4t} textgreater 0\\ 4t^2-9t+5 textgreater 0\\ 4t^2-4t-5t+5 textgreater 0\\ 4t(t-1)-5(t-1) textgreater 0\\ (4t-5)(t-1) textgreater 0$

$(t-frac{5}{4})(t-1) textgreater 0 and t textgreater 0\\ +++++++(1)-------(frac{5}{4})++++++ textgreater t\\ tin(0; 1)cup(frac{5}{4}; +infty)\\ 0 textless (frac{5}{4})^x textless 1 or (frac{5}{4})^x textgreater frac{5}{4}\\ (frac{5}{4})^x textless (frac{5}{4})^0 or (frac{5}{4})^x textgreater (frac{5}{4})^1\\ x textless 0 or x textgreater 1\\ xin(-infty; 0)cup(1; +infty)$

Ответ: $(-infty; 0)cup(1; +infty)$