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If AM of two numbers is twice of their GM, then the ratio of greatest number to smallest number is

Options

  1. A7 - 4 3
  2. B7 + 4 3
  3. C21
  4. D5

Correct answer

B. 7 + 4 3

Step-by-step solution

Let the numbers be x and y Since, x + y 2 = 2 x y ⇒ x + y = 4 x y .....(i) ⇒ x + y 2 = 16 x y Also x - y 2 = x + y 2 - 4 x y ∴ x - y 2 = 16 x y - 4 x y = 12 x y ⇒ x - y = 2 3 x y ...(ii) On solving Eqs. (i) and (ii), we get x = ( 2 + 3 ) x y and y = ( 2 - 3 ) x y ∴ Required ratio = x y = ( 2 + 3 ) x y ( 2 - 3 ) x y = 2 + 3 2 = 7 + 4 3

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