The Inequality Inspired by Joel Tan 2

Algebra Level 5

Let \(x, y, z\geq 0\) be reals such that \(x+y+z=1\).

Find the maximum possible value of

\[x (x+y)(y+z)^6(x+z)^2\]

The answer can be written as \(\dfrac {a^x}{b^y}\) for positive integers \(a, b, x, y\), where \(a, b\) are as small as possible. Find \(a+b+x+y\).



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