Question 33
For real numbers $a$, $b$ and $c$ we have
$$
(2b - a)^2 + (2b - c)^2 = 2(2b^2 - ac).
$$
Prove that the numbers $a$, $b$ and $c$ are three consecutive terms in some arithmetic sequence.
$$
(2b - a)^2 + (2b - c)^2 = 2(2b^2 - ac).
$$
Prove that the numbers $a$, $b$ and $c$ are three consecutive terms in some arithmetic sequence.