Problem 29

Algebra Level 5

( x + y + z ) 5 x 4 ( y + z ) + y 4 ( z + x ) + z 4 ( x + y ) \large \frac{(x+y+z)^{5}}{x^4(y+z)+y^4(z+x)+z^4(x+y)}

Given that x , y , z x,y,z are non-negative. Find the minimum value of the expression above.


Not an original problem.
This problem is in this Set .


The answer is 12.

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