Question

The terms $\frac{1}{\sqrt{5}+\sqrt{6}},\frac{1}{\sqrt{6}+\sqrt{4}},\frac{1}{\sqrt{4}+\sqrt{5}}$ are in

• A. A.P.
• B. G.P.
• C. H.P.
• D. A.G.P.

Answer 1

The correct option is A A.P.

$\frac{\frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{4}+\sqrt{5}}}{2}=\frac{1}{\sqrt{6}+\sqrt{4}}\frac{\sqrt{5}-\sqrt{6}}{-1}+\frac{\sqrt{4}-\sqrt{5}}{-1}=\frac{2(\sqrt{6}-\sqrt{4})}{6-4}-\sqrt{5}+\sqrt{6}+\sqrt{5}-\sqrt{4}=\sqrt{6}-\sqrt{4}\sqrt{6}-\sqrt{4}=\sqrt{6}-\sqrt{4}$

LHS=RHS

$\frac{1}{\sqrt{5}+\sqrt{6}},\frac{1}{\sqrt{4}+\sqrt{5}},\frac{1}{\sqrt{6}+\sqrt{4}}$ are in AP