A) A.P.
B) G.P.
C) H.P.
D) None of these
Correct Answer: A
Solution :
a, b, c are in A.P. i.e., 2b = a + c Let \[\frac{1}{\sqrt{a}+\sqrt{c}}-\frac{1}{\sqrt{a}+\sqrt{b}}=\frac{1}{\sqrt{b}+\sqrt{c}}-\frac{1}{\sqrt{a}+\sqrt{c}}\] Þ \[\frac{\sqrt{b}-\sqrt{c}}{\sqrt{a}+\sqrt{b}}=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{b}+\sqrt{c}}\]\[\Rightarrow b-c=a-b\]Þ\[2b=a+c\] \[\therefore \frac{1}{\sqrt{a}+\sqrt{b}},\frac{1}{\sqrt{a}+\sqrt{c}},\frac{1}{\sqrt{b}+\sqrt{c}}\] are in A.P.
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