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

Explanation

let two number be a, b

given that `(a+b)/2 = 6` --eqn(1)

also, `G^2 + 3*H = 48`

so, `a*b + 3*(2*a*b)/(a+b) = 48 `

`a*b + (3*a*b)/6 = 48`

`ab(1+ 1/2) =48 `

`ab(3/2) = 48`

`ab= (48*2)/3 = 32`

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