Question 25
We say that the triple $a, b, c$ from the segment $[-1; 1]$ is *worthy*, if these numbers satisfy the inequality $1 + 2abc \gt a^2 + b^2 + c^2$. Prove that if the triples $a, b, c$ and $x, y, z$ are worthy, then $ax, by, cz$ is worthy as well.
(Voloshyn Denys)
(Voloshyn Denys)