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: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: 9Â
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