Suppose that *x*, *y*, and *z* are positive real numbers with *x*+*y*+*z*=1. Then find (without calculus) the minimum value of .

Here, we can use the AM-GM inequality:

and

,

but , so

,

and so

and so , with equality when .

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Tags: AM-GM Inequality, Arithmetic Mean, Geometric Mean, Math, Minimum Value, Monday Math

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