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Method and examples
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Geometric Progression |
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Problem 9 of 23 |
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9. Two numbers are in the ratio : and difference of arithmetic mean and geometric mean is , then find that numbers
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Solution
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Solution provided by AtoZmath.com
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This is demo example. Please click on Find button and solution will be displayed in Solution tab (step by step)
| 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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