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

Question

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