Question

For some positive and distinct real numbers \(x ,y\), and \(z\) , if \(\frac{1}{\sqrt{ y}+ \sqrt{z}}\) is the arithmetic mean of \(\frac{1}{\sqrt{x}+ \sqrt{z}}\) and \(\frac{1}{\sqrt{x} +\sqrt{y}}\) , then the relationship which will always hold true, is

• A. \(y ,x\), and \(z\) are in arithmetic progression
• B. \(\sqrt{x}, \sqrt{y}\) , and \(\sqrt{z}\) are in arithmetic progression
• C. \(x ,y\), and \(z\) are in arithmetic progression
• D. \(\sqrt x, \sqrt z\) , and \(\sqrt y\) are in arithmetic progression