USAMO problem

Algebra Level 3

Which of the following set of values of ( a , b , c , d ) (a,b,c,d) (in that order) minimizes the expression a b 3 + 4 + b c 3 + 4 + c d 3 + 4 + d a 3 + 4 \dfrac a{b^3+4} + \dfrac b{c^3+4} + \dfrac c{d^3+4} + \dfrac d{a^3+4} where a , b , c , d a,b,c,d are non-negative real numbers satisfying a + b + c + d = 4 a+b+c+d=4 ?

( 1 , 1 , 1 , 1 ) (1,1,1,1) ( 1 , 3 , 0 , 0 ) (1,3,0,0) ( 2 , 1 , 3 , 3 ) (2,1,3,3) ( 2 , 2 , 0 , 0 ) (2,2,0,0)

Wadie Education by wadie education , 16, Morocco

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