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The geometric mean and harmonic mean of two nonnegative observations are 10 and 8 respectively. Then what is the arithmetic mean of the observations equal to?

Options

  1. A4
  2. B9
  3. C12.5
  4. D25

Correct answer

C. 12.5

Step-by-step solution

aligned a b & =10 a b & =100 2 a b a+b & =8 200 a+b & =8 a+b & =25 (a-b)^2 & =(a+b)^2-4 a b & =625-400 & =225 a-b & =15 a+b & =25 2 a & =40 a & =20, b=5 A.M. & = 20+5 2 =12.5 . aligned

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