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Geometric Progression 



Problem 9 of 23 


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










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Geometric Progression 
9. 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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