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Two numbers are in the ratio 9 : 16 and difference of arithmetic mean and geometric mean is 1 , then find that numbers

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Your problem `->` Two numbers are in the ratio 9 : 16 and difference of arithmetic mean and geometric mean is 1 , then find that numbers


Here ratio of the two terms is `9:16`.

Let the two terms be `9x` and `16x`.

Now difference of their Arithmetic mean `A` and Geometric mean `G` is `1`.

`=> A - G = 1` (Because `A` > `G`).

`=> (9x + 16x)/2 - sqrt(9x × 16x) = 1`.

`=> (25x)/2 - sqrt(144) x = 1`.

`=> x = 2`

`=>` The required two terms are `9 × 2` and `16 × 2`.

`=>` The required two terms are `18` and `32`.






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