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Let a, b, c be positive real numbers. The following system of equations in x, y and z (x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(c^2)=1, (x^2)/(a^2)-(y^2)/(b^2)+(z^2)/(c^2)=1,(-x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(c^2)=1 has

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