Question

Найдите сумму целых решений неравенства

$log_{log _{3}2}(x^2-12x+36)geq 0$

Answer 1

$\x^2-12+36>0\ (x-6)^2>0\ xinmathbb{R}setminus{6}\\ log_{log _{3}2}(x^2-12x+36)geq 0\ x^2-12x+36leq (log_3 2)^0\ x^2-12x+36leq1\ x^2-12x+35leq0\ x^2-7x-5x+35leq0\ x(x-7)-5(x-7)leq0\ (x-5)(x-7)leq0\ xinlangle5,7rangle\\ x inlangle5,7ranglewedge xinmathbb{R}setminus{6}\xinlangle5,6)cup(6,7rangle\\ xin(langle5,6)cup(6,7rangle) cap mathbb{Z}\ x={5,7}\\ 5+7=underline{12}$