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Method and examples
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Geometric Progression |
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Problem 8 of 23 |
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8. Arithmetic mean of two number is 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 |
8. Arithmetic mean of two number is 13 and geometric mean is 12 , then find that numbers
Let the two terms be `a` and `b`.
`=> A = (a + b)/2 = 13` and `G = sqrt(ab) = 12`
`=> a + b = 26 ->(1)` and `ab = 144 ->(2)`
`=> b = 26 - a ->(3)`
Now putting the value of `(3)` in `(2)`, we get
`a(26 - a) = 144`
`=> 26a - a^2 = 144`
`=> a^2 - 26a + 144 = 0`
`=> (a - 8)(a - 18) = 0`
`=> a = 8` or `a = 18`
`=> a = 8 => b = 26 - a = 26 - 8 = 18`
and `a = 18 => b = 26 - a = 26 - 18 = 8`
`:.` Required numbers are `8` and `18`
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