The value is=?

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1 Answer
Jun 26, 2018

The Right Option is (4) : (5sqrt6)/12(4):5612.

Explanation:

Let, a,b in RR^+" such that, "a > b.

Their "AM"=(a+b)/2," and the GM"=sqrt(ab).

It is given that, (a+b)/2=5sqrt(ab).

:. (a+b)=10sqrt(ab).

:. (a+b)^2=100ab........................(ast^1).

Further, (a-b)^2=(a+b)^2-4ab.

=100ab-4ab..........[because, (ast^1)].

:. (a-b)^2=96ab..............................(ast^2).

From (ast^1) and (ast^2), we have,

(a+b)^2/(a-b)^2=(100ab)/(96ab)=25/24.

:. (a+b)/(a-b)=+sqrt(5^2/(2^2*6))............[because, (a-b) gt 0],

=5/(2sqrt6)*sqrt6/sqrt6.

rArr (a+b)/(a-b)=(5sqrt6)/12, showing that,

The Right Option is (4) : (5sqrt6)/12.