Найдите область определения функции y=корень из (x^2+12x+20)/(2x-52).

\[y = \frac{\sqrt{x^{2} + 12x + 20}}{2x - 52}\]

\[x^{2} + 12x + 20 \geq 0\]

\[x_{1} + x_{2} = - 12;\ \ \ x_{1} \cdot x_{2} = 20\]

\[x_{1} = - 10;\ \ x_{2} = - 2\]

\[(x + 10)(x + 2) \geq 0.\]

\[2x - 52 > 0\]

\[2x > 52\]

\[x > 26.\]

\[Ответ:x \in ( - \infty; - 10\rbrack \cup \lbrack - 2;26) \cup (26; + \infty).\]