Nice Equation
Let a, b, c, x, y, and z be positive real numbers. How many solutions of this equation : a 2 b x 3 + y 3 + z 3 + b 2 c x 3 + y 3 + z 3 + c 2 a x 3 + y 3 + z 3 = a 2 b c + b 2 c a + c 2 a b 2 7 x y z 3 a b c
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