Решите неравенство (x^2-12x+35)/(x-6)^2<0.

Ответ:

\[\frac{x^{2} - 12x + 35}{(x - 6)^{2}} < 0\]

\[x^{2} - 12x + 35 = 0\]

\[D = 36 - 35 = 1\]

\[x_{1} = 6 - 1 = 5;\ \ x_{2} = 6 + 1 = 7.\]

\[\frac{(x - 5)(x - 7)}{(x + 6)(x - 6)} < 0\]

\[Ответ:\ x \in (5;6) \cup (6;7).\]