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Black Book Advanced Problems in MathematicsMathematicsQuadratic Equation

Let x, y and z are positive reals and x^2 + xy + y^2 = 2 ; y^2 + yz + z^2 = 1 and z^2 + zx + x^2 = 3 . If the value of xy + yz + zx can be expressed as p q where p and q are relatively prime positive integer find the value of p - q :

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