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inequality questionfest

Algebra Level 2

Given positive reals \( a, b, c \) such that \( a + b + c = 4 \), what is the maximum value of

\[ a^2bc + ab^2c + abc^2? \]

\[ \frac{55}{23} \] \[ \frac{100}{63}\] \[4\] \[ \frac{256}{27} \]

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by madhav srirangan

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