1. ## geometric mean

The arithmetic mean of 1/(a+b) and 1/(b+c) is 1/(a+c)

Find in terms of b , the arithmetic mean of a^2 and c^2 .

2. Arithmetic mean implies

$\frac{\frac{1}{a+b} + \frac{1}{b+c}}{2} = \frac{1}{a+c}$

In this equation find a common denominator for the LHS, cross multiply then simplify.

After some cancelling you will be left with $a^2+c^2 = \dots$

$b^2$