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Algebra Level 5

How many ordered quadruples of non-negative real numbers are there that satisfies:

a+b+c+d=4a2bc+b2cd+c2da+d2ab=4 \begin{aligned} a + b + c + d = 4 \\ a^2bc + b^2cd + c^2da + d^2 ab = 4 \\ \end{aligned}


Now prove this.

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