The arithmetic mean of two numbers is 6 and their geometric mean G andharmonic mean H satisfy the relation `G^2+3H=48`.Find the two numbers.

The arithmetic mean of two numbers is 6 and their geometric mean G and

1.	The arithmetic mean of two numbers is 6 and their geometric mean G andharmonic mean H satisfy the relation `G^2+3H=48`.Find the two numbers.
Answer» let two number be a, b given that `(a+b)/2 = 6` --eqn(1) also, `G^2 + 3H = 48` so, `ab + 3(2ab)/(a+b) = 48 ` `ab + (3ab)/6 = 48` `ab(1+ 1/2) =48 ` `ab(3/2) = 48` `ab= (48*2)/3 = 32` so, a = 8 , b=4As, `(a+b)/2` = `(8+4)/2 = 6` is also satisfied.

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The arithmetic mean of two numbers is 6 and their geometric mean G andharmonic mean H satisfy the relation `G^2+3H=48`.Find the two numbers.

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