Question 164
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 harmonic average of the numbers $a$, $c$ is equal to the number $b$, so $b = \frac{2}{\frac{1}{a}+\frac{1}{c}}$. Is it necessary that the numbers $a$, $b$, $c$ are equal?
(Bogdan Rublyov)
(Bogdan Rublyov)