If `A` be one A.M. and `p ,q` be two G.M. `' s` between two numbers, then `2A` is equal to (a)`(p^3+q^3)/(p q)` (b) `(p^3-q^3)/(p q)` (c) `(p^2+q^2)/2` (d) `(p q)/2`

Explanation

Let the two numbers are `x` and `y`.

Then,

As `A` is the A.M. between `x` and `y`,

`A = (x+y)/2 =>2A = x+y->(1)`

As, `p` and `q` are the geometric mean of `x` and `y,`

`:. p^2 = qx and q^2 = py`

`=>x= p^2/q and y = q^2/p`

Putting these values in (1),

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