If the A.M. of two positive numbers `aa n db(a > b)` is twice their geometric mean. Prove that : `a : b=(2+sqrt(3)):(2-sqrt(3))dot`

Explanation

It is given that A.M. is twice of the G.M.

`:. (a+b)/2 = 2sqrt(ab)`

`=>(a+b)/(2sqrt(ab)) = 2/1`

Using componendo and dividendo,

`=>(a+b+2sqrt(ab))/(a+b-2sqrt(ab)) = (3+1)/(3-1)`

`=>(sqrta+sqrtb)^2/(sqrta-sqrtb)^2 = 3/1`

`=>(sqrta+sqrtb)/(sqrta-sqrtb) = sqrt3/1`

Using componendo and dividendo again,

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