The Inequality Inspired by Joel Tan 2

Algebra Level 5

Let x,y,z0x, y, z\geq 0 be reals such that x+y+z=1x+y+z=1.

Find the maximum possible value of

x(x+y)(y+z)6(x+z)2x (x+y)(y+z)^6(x+z)^2

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



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