# Not a harmonic mean question

**Algebra**Level 4

Let \(x, y, z\geq 0\) be reals such that \(x+y+z=1\). Find the maximum possible value of

\[x (x+y)^{2}(y+z)^{3}(x+z)^{4}.\]

Let \(x, y, z\geq 0\) be reals such that \(x+y+z=1\). Find the maximum possible value of

\[x (x+y)^{2}(y+z)^{3}(x+z)^{4}.\]

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