# Problem 39

Algebra Level 5

Consider an equation $$x^4+ax^3+bx^2+cx+d = 0$$ with roots (of $$x$$) $$x_1,x_2,x_3$$ and $$x_4$$. If $$x_1^{2016} + x_2^{2016} + x_3^{2016} + x_4^{2016} = 4$$, find the maximum value of $$a$$, $$a_{\text{max}}$$.

Submit your answer as $$a_{\text{max}} +b+c+d+x_1+x_2+x_3+x_4$$ when $$a_{\text{max}}$$ is fulfilled.

Set.

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