Home Competitions CR-MO 2016 A1
Find all solutions of the system y z 4 x 2 3 + 2 w x = 0 \sqrt[3]{\frac{yz^4}{x^2}}+2wx=0 3 x 2 y z 4 + 2 w x = 0 x z 4 y 3 + 5 w y = 0 \sqrt[3]{\frac{xz^4}{y}}+5wy=0 3 y x z 4 + 5 w y = 0 x y x 3 + 7 w z − 1 / 3 = 0 \sqrt[3]{\frac{xy}{x}}+7wz^{-1/3}=0 3 x x y + 7 w z − 1/3 = 0 x 12 + 125 4 y 5 + 343 2 z 4 = 16 x^{12}+\frac{125}{4}y^5+\frac{343}{2}z^4=16 x 12 + 4 125 y 5 + 2 343 z 4 = 16 x , y , z ≥ 0 x, y, z \ge 0 x , y , z ≥ 0 w ∈ R w \in R w ∈ R
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