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      Question

      The arithmetic mean and geometric mean of two numbers

      are 7 and 2√10 respectively, then find the numbers.
      A 2, 20 Correct Answer Incorrect Answer
      B 5, 4 Correct Answer Incorrect Answer
      C 4, 10 Correct Answer Incorrect Answer
      D 8, 5 Correct Answer Incorrect Answer

      Solution

      Arithmetic Mean = 7   (x + y)/2 = 7 x + y = 14                            ----(1) Geometric Mean = 2√10 √ xy = 2√ 10 Now, xy = (2√ 10)2 = 40 ------(2) (x - y) ² = (x + y) ² - 4xy   (x - y) ² = 142 - (4 x 40)   (x - y) ² = 196 - 160 = 36 x - y = 6              ----(3) Now, adding equation (1) and (3) we get   2x = 20   x = 10 and y =4. (10,4)

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