Answer :

Let the two numbers be a and b.


GM = √ab


According to the given condition,



a + b = 4√ab …(1)


(a + b)2 = 16ab


Also,


(a – b)2 = (a + b)2 – 4ab


= 16ab – 4ab


= 12ab


a – b = 2√3ab…(2)


Adding (1) and (2), we obtain


2a = (4 + 2√3 )√ab


a = (2 + √3)√ab


substituting the value of a in (1), we obtain,


b =(2 – √3)√ab



Thus, the required ratio is (2+√3) : (2–√3).


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