8-3. Find all common points of the graphs

$$
y=8 \cos \pi x \cdot \cos 2 \pi x \cdot \cos ^{2} 4 \pi x \quad \text { and } \quad y=\cos 11 \pi x
$$

with abscissas belonging to the interval $[0 ; 1]$. In the answer, specify the sum of the abscissas of the found points.
Solution. This is equivalent to $\sin 4 \pi x=\sin (-10 \pi x), x \neq n, n \in \mathbb{Z}$. From this, $x=k / 7$ or $x=1 / 6+l / 3, k, l \in \mathbb{Z}$.

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

Answer: 4,5 .