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      Question

      If x, y and z are positive numbers and x + y + z = 1,

      then the least value of 1/x + 1/y + 1/z is:
      A 7 Correct Answer Incorrect Answer
      B 5 Correct Answer Incorrect Answer
      C 9 Correct Answer Incorrect Answer
      D 11 Correct Answer Incorrect Answer

      Solution

      For positive (x, y, z) with (x + y + z = 1), the expression ({1/x} + {1/y} + {1/z}) is minimized when (x = y = z) (by symmetry and AM-HM inequality).  Substitute (x = y = z = {1/3}):  [{1/x} + {1/y} + {1/z} = 3 + 3 + 3 = 9]  Least value: 9 

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