Question 170
It is known that the arithmetic average of the numbers $a$, $b$ is equal to the number $c$, so $c = \frac{1}{2}(a+b)$, and that the geometric average of the numbers $a$, $c$ is equal to the number $b$, so $b = \sqrt{ac}$. Is it necessary that the numbers $a$, $b$, $c$ are equal?