Task 3. Option I.

For what values of the parameter $a$ does the function $y=\frac{5}{x^{2}-2 x+20}$ decrease on the interval $[2 a ; 2-a]?$
Solution. The given function is decreasing on the interval $[1 ;+\infty)$. The function will be decreasing on the interval $[2 a ; 2-a]$ if the conditions of the system are satisfied

$\left\{\begin{array}{l}2 a \geq 1, \\ 2-a>2 a\end{array} \Leftrightarrow \frac{1}{2} \leq a<\frac{2}{3}\right.$.

Answer: $a \in\left[\frac{1}{2} ; \frac{2}{3}\right)$.