If \(x + y = 9\) and \(x^2 + y^2 = 65\), find xy.
8
Using the identity \((x+y)^2 = x^2 + y^2 + 2xy\), we can isolate \(xy\).
Substituting the given values: \(9^2 = 65 + 2xy\), so \(81 = 65 + 2xy\).
This gives \(2xy = 16\), so \(xy = 8\).
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