Question

${7}^{2x} - 6 \times {7}^{x} + 5 > 0$
Помогите решить неравенство​

Answer 1

$7^{2x}-6\cdot 7^{x}+5>0\\\\(7^{x})^2-6\cdot 7^{x}+5>0\\\\t=7^{x}>0\; \; \to \; \; \; t^2-6t+5>0\\\\t^2-6t+5=0\; \; \to \; \; t_1=1\; ,\; \; t_2=5\; \; (teorema\; Vieta)\\\\(t-1)(t-5)>0\qquad +++(1)---(5)+++\\\\t\in (-\infty ,1)\cup (5,+\infty )\\\\\left [ {{t<1} \atop {t>5}} \right.\; \; \left [ {{7^{x}<1} \atop {7^{x}>5}} \right.\; \; \left[{ {{7^{x}<7^0\; \; \; \; \; } \atop {7^{x}>7^{log_75}}} \right.\; \; \left [ {{x<0\quad } \atop {x>log_75}} \right. \\\\Otvet:\; \; x\in (-\infty ,0)\cup (log_75,+\infty )\; .$