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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class11  >>  Sequence and Series

If AM and GM of two numbers are in ratio $p : q$, then the ratio of two numbers is

$(a)\;p-\sqrt{p^2+q^2} : p+\sqrt{p^2+q^2}\qquad(b)\;p+\sqrt{p^2+q^2} : p-\sqrt{p^2+q^2}\qquad(c)\;p : q\qquad(d)\;p+\sqrt{p^2-q^2} : p-\sqrt{p^2-q^2}$

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Answer : (d) $\;p+\sqrt{p^2-q^2} : p-\sqrt{p^2-q^2}$
Explanation : AM : GM = p : q
$\large\frac{x+y}{2} : \sqrt{xy} = p : q$
$\large\frac{x+y}{2p}=\large\frac{\sqrt{xy}}{q}=k (say)$
$x : y= p+ \sqrt{p^2-q^2}: p-\sqrt{p^2-q^2}\;.$
answered Jan 23, 2014 by yamini.v

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