5

Part of 1999 Canada National Olympiad

Problems(1)

inequalities: x^2 y + y^2 z + z^2 x <= 4/27 if x + y + z = 1

Source: CMO (Canada MO) 1999, problem 5

x

y

z

be non-negative real numbers satisfying x \plus{} y \plus{} z \equal{} 1. Show that x^2 y \plus{} y^2 z \plus{} z^2 x \leq \frac {4}{27} and find when equality occurs.

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