Question

17 задание, показательное неравенство решите пожалуйста!!!!

Answer 1

$\frac{31-7\cdot 5^{x}}{25^{x}-30\cdot 5^{x}+125} \geq 0,25\\\\t=5^{x}\ \textgreater \ 0,\; \; \frac{31-7t}{t^2-30t+125} -\frac{1}{4} \geq 0\\\\\frac{124-28t-t^2+30t-125}{4(t^2-30t+125)} \geq 0\\\\t^2-30t+125=0\; \; \to \; \; t_1=5; t_2=25\; \; (teor.\; Vieta)\\\\\frac{-(t^2-2t+1)}{4(t-5)(t-25)} \geq 0\; ,\; \; \frac{(t-1)^2}{(t-5)(t-25)} \leq 0\\\\+++(1)+++(5)---(25)+++\\\\t\in (5,25)\; \; \left \{ {{5^{x}\ \textgreater \ 5} \atop {5^{x}\ \textless \ 25\; (25=5^2)}} \right. \; \; \left \{ {{x\ \textgreater \ 1} \atop {x\ \textless \ 2}} \right. \\\\x\in (1,2)$