10. (20 points) Find all values of the parameter $a$ for which the equation

$$
5|x-4 a|+|x-a^{2}|+4 x-3 a=0
$$

has no solution.
Answer: $(-\infty ;-9) \cup(0 ;+\infty)$

## Innopolis Open

Mathematics Olympiad

Innopolis University

## Qualifying (correspondence) stage in mathematics, December 2, 2018

## 11th grade, variant 2.