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Arithmetic mean of two number is 13 and geometric mean is 12 , then find that numbers

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Your problem `->` 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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