A) \[\frac{7\sqrt{3}}{12}\]
B) \[\frac{3\sqrt{2}}{4}\]
C) \[\frac{\sqrt{6}}{2}\]
D) \[\frac{5\sqrt{6}}{12}\]
Correct Answer: D
Solution :
\[\frac{a+b}{2}=5\sqrt{ab}\] \[\frac{a+b}{\sqrt{ab}}=10\] \[\therefore \] \[\frac{a}{b}=\frac{10+\sqrt{96}}{10-\sqrt{96}}=\frac{10+4\sqrt{6}}{10-4\sqrt{6}}\] Use C and D \[\frac{a+b}{a-b}=\frac{20}{8\sqrt{6}}=\frac{5}{2\sqrt{6}}=\frac{5\sqrt{6}}{12}\]
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