# 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 $$a+b+x+y$$.

Inspiration

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