Task B-3.3. If for the lengths of the sides of a certain triangle it holds that $a^{2}+2 b^{2}+3 c^{2}=2 a c+4 b c$, calculate the angles of that triangle.
Solution. Let's write the given equality in the following form

$$
\begin{array}{r}
a^{2}-2 a c+c^{2}+2 b^{2}-4 b c+2 c^{2}=0 \\
(a-c)^{2}+2 \cdot(b-c)^{2}=0
\end{array}
$$

This is possible only for $a=b=c$, so all three angles are equal to $60^{\circ}$.