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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