A) AP
B) GP
C) HP
D) AP and HP
E) AP and GP
Correct Answer: A
Solution :
\[\because \] \[\frac{1}{\sqrt{z}+\sqrt{x}}-\frac{1}{\sqrt{x}+\sqrt{y}}\] \[=\frac{1}{\sqrt{y}+\sqrt{z}}-\frac{1}{\sqrt{z}+\sqrt{x}}\] \[\Rightarrow \] \[y-z=x-y\] \[\Rightarrow \] \[y=\frac{z+x}{2}\] \[\Rightarrow \] \[x,\text{ }y,\text{ }z\]are in AP Hence, \[\frac{1}{\sqrt{x}+\sqrt{y}},\frac{1}{\sqrt{z}+\sqrt{x}},\frac{1}{\sqrt{y}+\sqrt{z}}\] are in AP.You need to login to perform this action.
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