The Inequality Inspired by Joel Tan

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)5(y+z)4(x+z)4x (x+y)^5(y+z)^4(x+z)^4

The answer can be written as aibjck\dfrac {a^i}{b^jc^k} for positive integers a,b,c,i,j,ka, b, c, i, j, k, where a,b,ca, b, c are as small as possible. Find a+b+c+i+j+ka+b+c+i+j+k.



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