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 \(c\).

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