Question

If the A.M. between a and b is m times their H.M. then a:b =

• A. $\sqrt{m}+\sqrt{m-1}:\sqrt{m}-\sqrt{m-1}$
• B. $\sqrt{m}-\sqrt{m-1}:\sqrt{m+1}+\sqrt{m-1}$
• C. $\sqrt{m}+\sqrt{m+1}:\sqrt{m}-\sqrt{m+1}$
• D. None of these

Answer 1

The correct option is D None of these

$Wehave\frac{a+b}{2}=m\frac{2ab}{a+b}Or\frac{(a+b{)}^2}{4ab}=m...\left(i\right)Or\frac{(a+b{)}^2}{4ab}-1=m-1Or\frac{(a-b{)}^2}{4ab}=m-1...\left(ii\right)Dividing\left(i\right)by\left(ii\right),weget\frac{(a+b{)}^2}{(a-b{)}^2}=\frac{m}{m-1}or\frac{a+b}{a-b}=\frac{\sqrt{m}}{\sqrt{m-1}}Applyingcompnedoanddividendo,Weget\frac{a}{b}=\frac{\sqrt{m}+\sqrt{m-1}}{\sqrt{m}-\sqrt{m-1}}$