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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).┬а Substitute (x = y = z = {1/3}):┬а [{1/x} + {1/y} + {1/z} = 3 + 3 + 3 = 9]┬а Least value: 9┬а

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