= 5200 + 2xy

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• x^2 + y^2 = 5200
• Plugging in the known values:
• 100^2 = 5200 + 2xy
• 2xy = 4800 \quad \Rightarrow \quad xy = 2400
• Now, we use another identity for cubes:
• We already know \( x + y = 100 \), \( x^2 + y^2 = 5200 \), and \( xy = 2400 \). So:

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