# AM and GM

Algebra Level 3

Let $$a,b$$ and $$c$$ follows an arithmetic progression.

Denote $$x$$ as the geometric mean of $$a$$ and $$b$$, and
denote $$y$$ as the geometric mean of $$b$$ and $$c$$.

Find the arithmetic mean of $$x^2$$ and $$y^2$$ in terms of $$a,b$$ and/or $$c$$.

×