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Geometric Progression 



Problem 8 of 23 


8. Arithmetic mean of two number is and geometric mean is , then find that numbers










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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`







