# Task 2. (10 points)

It is known that the graph of the function $f(x)=x^{2}-2016 x+2015$ passes through two different points with coordinates ( $a, c$ ) and ( $b, c$ ). Find the sum $a+b$.

#
# Solution

According to the problem,

$$
\begin{gathered}
f(a)=a^{2}-2016 a+2015=f(b)=b^{2}-2016 b+2015 \Leftrightarrow \\
\Leftrightarrow a^{2}-b^{2}=2016 a-2016 b \Leftrightarrow(a-b)(a+b)=2016(a-b) \Leftrightarrow a+b=2016
\end{gathered}
$$

Answer: 2016.