# Roots progression?

Algebra Level 3

If $$\color{red}a , \color{blue}b , \color{purple}c$$ are in Arithmetic Progression. Then $$\dfrac{1}{\sqrt{\color{blue}b} + \sqrt{\color{purple}c}} , \dfrac{1}{\sqrt{\color{purple}c} + \sqrt{\color{red}a}} , \dfrac{1}{\sqrt{\color{red}a} + \sqrt{\color{blue}b}}$$ are in ..................

Clarification : $$\color{red}a , \color{blue}b , \color{purple}c > 0$$

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