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Suppose xxx and yyy are real numbers such that x2x^2x2 and y2y^2y2 are positive integers.
Find the maximum value of x2−xyx^2-xyx2−xy if (3x2−y2)2+(x2+y2)2=72\left(3x^2-y^2\right)^2+\left(x^2+y^2\right)^2=72(3x2−y2)2+(x2+y2)2=72.
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