8-2. Find all common points of the graphs

$$
y=8 \cos ^{2} \pi x \cdot \cos 2 \pi x \cdot \cos 4 \pi x \quad \text { and } \quad y=\cos 6 \pi x
$$

with abscissas belonging to the interval $[-1 ; 0]$. In your answer, specify the sum of the abscissas of the found points.
Solution. This is equivalent to $\sin 9 \pi x=\sin (-5 \pi x), x \neq n, n \in \mathbb{Z}$. From this, $x=k / 7$ or $x=1 / 4+l / 2, k, l \in \mathbb{Z}$.

The roots of the equation in the interval $[-1 ; 0]$ are: $-1 / 7,-2 / 7,-3 / 7,-4 / 7,-5 / 7,-6 / 7$ and $-1 / 4,-3 / 4$.

Answer: -4 .