Inequalities # 1

Algebra Level 4

Let a,b,c,da,b,c,d be positive real numbers. Also ab+bc+cd+da=1ab+bc+cd+da=1. Then find the minimum value of a3b+c+d+b3a+c+d+c3a+b+d+d3a+b+c\large\dfrac{a^3}{b+c+d} + \dfrac{b^3}{a+c+d}+ \dfrac{c^3}{a+b+d}+ \dfrac{d^3}{a+b+c} If your answer is of the form AB\dfrac{A}{B} , where AA and BB are positive coprime integers. Then enter the value of A+BA+B.

Source: RMO training camp 2016

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