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BITSAT2024MathematicsSequences and SeriesActual

If arithmetic mean of two distinct positive real number a and b(a b) be twice their geometric mean, then a: b=

Options

  1. A(2+ 3 ):(2- 3 )
  2. B(2+ 5 ):(2- 5 )
  3. C(2+ 2 ):(2- 2 )
  4. DNone of these

Correct answer

A. (2+ 3 ):(2- 3 )

Step-by-step solution

By the given condition, a+b 2 =2 a b a+b=4 a b Now, (a-b)^2=(a+b)^2-4 a b=16 a b-4 a b=12 a b a-b= 12 a b =2 3 a b . (Taking + ve sign only as a b ) a+b a-b = 4 a b 2 3 a b = 2 3 By componendo and dividendo, 2 a 2 b = 2+ 3 2- 3 or a b = 2+ 3 2- 3

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