Q. 283.7( 75 Votes )

The sum of

Answer :

Let the two numbers be a and b.


G.M. = √ab


According to the given condition,


a + b = 6√ab


squaring on both sides we get,


(a + b)2 = 36(ab) —1


Here,


(a—b)2 = (a + b)2 – 4ab = 36ab – 4ab = 32ab


a—b = √32√ab = 4√2√ab —2


Adding eq(1) and eq(2), we get


2a = (6 + 4√2)√ab


a = (3 + 2√2)√ab


Substituting the value of a in eq(1), we obtain


b = 6√ab – (3 + 2√2)√ab


b = (3 — 2√2)√ab


Now,



The required ratio is


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